Linebackers Tedy Bruschi, left, and Junior Seau could be rejoicing over big defensive plays with the Patriots again next season if they decide to keep playing football.

The Providence Journal Glenn Osmundson

FOXBORO — The New England Patriots coaching staff will be taking a good hard look at its team over the next few weeks to try to figure out how to improve for next season.

That’s a scary thought for their opponents because the Patriots were one of the best teams, perhaps ever, in the regular season, going 16-0, setting the NFL record for points scored (589), most touchdowns (75), most touchdowns thrown by a quarterback (Tom Brady, 50) and most touchdown receptions (Randy Moss, 23).

There are 13 unrestricted free agents on the Patriots roster, and the team hopes to keep some of them.

A few of them were invaluable to the team last season both on and off the field — Moss, linebackers Tedy Bruschi and Junior Seau, and defensive back Asante Samuel.

Others did not play as big a role in the Patriots’ pursuit of perfection — receiver Troy Brown, defensive lineman Rashad Moore, and defensive backs Chad Scott and Mel Mitchell.

And some, as far as re-signing goes, are teetering on the fence — receiver Jabar Gaffney, defensive back Randall Gay, linebacker Larry Izzo, defensive back Eugene Wilson, and long snapper Lonie Paxton.

“[The] first thing is to go back and look at what happened during the season, evaluate our team and our scheme and our players,” New England coach Bill Belichick said this week on what’s next for the Patriots coaching staff.

“Then we start moving into the team-building aspect, free agency, the draft, personnel decisions, playbook and all the things that we do prepare for the offseason program, the spring camps and ultimately the ’08 season.”

So which free agents will the Patriots try to retain for next year?

Looking at the list above, Moss is the first free agent that the Patriots will probably aggressively try to keep. Along with his record-setting 23 touchdown catches, he made 98 receptions for 1,493 yards.

As the Patriots primary deep threat, Moss demanded double and sometimes triple teams, which gave his teammates the chance to get open on one-on-one coverage underneath.

Moss, who took a major pay cut to join the Patriots this season ($3-million base salary plus bonuses) said he wanted to be in a Patriots uniform next season.

“I’m still loving what I do and being here, being a New England Patriot. I think this is where I do want to be,” Moss said before the Super Bowl. “Hopefully, we can work something out after this season is over. The sky is the limit. I really don’t know if I’m going to be a New England Patriot, but to answer your question, I would love to retire a Patriot, yes.”

So will Moss be back?

You’ll probably know in the next couple of weeks inasmuch as he is a primary candidate for the franchise tag, and the 15-day period in which teams can assign the franchise tag to a player began yesterday.

The Patriots can lock him up for one year with the franchise tag at $7.848 million, which represents the average salary-cap charge of the highest-paid five receivers in 2007.

No. 2 on the Patriots pecking order is probably Samuel, who teammate Rodney Harrison calls the “best cornerback in the league — hands down.”

Samuel, who has a team-leading 16 interceptions over the last two seasons, says he wants to remain a Patriot but, it will take a mega-deal to sign him. Considering the Patriots’ past with players wanting blockbuster deals, they will probably pass on him.

Still, Samuel is a proven playmaker in the secondary.

“He has done a great job for us all year at corner,” Belichick said of Samuel before the Super Bowl. “He has given us a very dependable and consistent level of play and come up with some big plays, both in pass defense and a lot of time when the ball doesn’t even get thrown to his man.”

Much of what happens with Bruschi and Seau will depend on their decisions to either keep playing football or retire. At this stage of the game, both Bruschi, 34, and Seau, 39, are playing to win championships, not so much for the money, so if they do decide to play football again, it will probably be in a Patriots uniform.

Both Bruschi and Seau said after the Super Bowl that they are going to take some time to decide whether they are going to return to football next season.

Receivers Donte Stallworth ($8 million) and Kelley Washington ($4 million) both have big options due this month that probably won’t be paid, so they will become free agents. That should make signing Gaffney a big priority.

Stallworth and Washington could return with different deals, however. Brown, who played in only one game this season, will probably retire.

If Samuel leaves, then re-signing Gay, the Patriots’ third cornerback this season, Wilson, who dropped down the Patriots depth chart late in the season, or Mitchell, who played mostly on special teams this year, could become a priority.

In addition, the Patriots must decide to either pay Paxton a minimum salary of $720,000 or see whether there is a rookie they could sign for $285,000 to free up money for another player.

Brady is not a free agent. He has three years left on his contract, but considering that Raiders quarterback JaMarcus Russell signed a six-year, $61-million deal, Brady might approach the Patriots about revamping his deal to make him one of the highest-paid quarterbacks in the league, which could affect everything else.

Brady has a reported $14.6-million salary-cap charge for 2008.

The annual scouting combine in Indianapolis begins Feb. 20, and the free-agency period is set to begin Feb. 29. Teams will have a salary cap of $116 million in 2008, an increase of $7 million 2007.

The Patriots signed guard Dan Connolly, wide receiver C.J. Jones, offensive lineman Jimmy Martin, and cornerback Tim Mixon to contracts this week.

Connolly, 25, Jones, 27, and Mixon, 23, all ended the season on the Patriots’ practice squad, and Martin, 25, spent the 2007 season out of football after being released by the Vikings on Sept. 2, 2007.LOOKING AHEAD

TOMORROW:

Which free agents will the Patriots pursue?

roblee@projo.com