Catcher Jason Varitek is one of two free-agent players that the Red Sox have offered salary arbitration to.

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The Providence Journal / Mary Murphy

As expected, the Red Sox last night announced that they have offered salary arbitration to free-agent catcher Jason Varitek and pitcher Paul Byrd.

Boston also announced it will not offer salary arbitration to pitchers Bartolo Colon, Curt Schilling and Mike Timlin, catcher David Ross, infielders Sean Casey and Alex Cora, and outfielder Mark Kotsay.

Varitek is a Type A free agent, which means if he does not accept the Sox’ offer — which he probably will not — and then signs with another club, the Red Sox will receive draft picks as compensation.

The team captain has until Sunday to decline or accept the offer.

This is the only time of the season when baseball has a time constraint.

As a policy, general manager Theo Epstein and the Red Sox refrain from discussing contract situations publicly.

Varitek did not make himself available for comment last night.

Under the terms of the collective-bargaining agreement, clubs retain the right to negotiate and/or enter into a contract agreement with any of their free agents, regardless of whether arbitration was offered. There are no deadlines for such negotiations and/or agreements.

Clubs had until midnight last night to offer its free agents arbitration. By not offering arbitration, teams forfeit draft-pick compensation if the player signs with another team.

Varitek, 36, has been with the Red Sox since 1997 and has been an integral part of the club, helping Boston win two World Series championships — in 2004 and 2007. Varitek’s last contract with the Red Sox — four years, $40 million — expired at the end of the 2008 season. He is represented by agent Scott Boras, who believes his veteran client is deserving of a long-term deal.

Varitek had a career-worst .220 average with only 13 home runs and 43 RBI last season. There’s no denying the fact he is one of the most respected and well-prepared catchers in baseball. He also proved that he’s durable. Discounting the 2001 and 2006 seasons in which he had injuries, Varitek has not played less than 131 games in a season since becoming the club’s starting catcher in 1999.

The Red Sox acquired Byrd from Cleveland in August to help the rotation. The veteran right-hander, who turns 38 tomorrow, combined for an 11-12 record with a 4.60 ERA between the two clubs.

In other news, the Red Sox have agreed to a three-year deal with Japanese pitcher Junichi Tazawa.

According to published reports, the Red Sox will make the official announcement this week that they have signed the 22-year-old hurler. Tazawa is on his way to Boston for a physical. The deal is worth a reported $3 million, and he will be placed on the Sox’ 40-man roster.

Other clubs were vying for his services, but one reason he decided to sign with the Red Sox is because fellow Japanese pitcher Daisuke Matsuzaka is his idol.

It was also reported the Red Sox signed left-handed pitcher Billy Traber to a minor-league deal. The 29-year-old reliever will be invited to big-league camp during spring training. He split time between the Yankees and their Triple-A affiliate Scranton in 2008.

jmcdonal@projo.com