NEW YORK — A potential move of spring training sites is gaining momentum, and before the end of October the Red Sox could have a deal in place to switch their Florida spring base from Fort Myers to Sarasota, starting in 2011.

Earlier this week, Sarasota County officials approved the purchase of 1.2 acres near downtown Sarasota, which gives the county and city control of about 8 acres that would be the site of a new ballpark to attract the Sox.

The Sox could then develop the area around the ballpark with restaurants, shops and hotels.

The latest move was viewed as a critical piece in the area’s efforts to bring the Sox back to the city that served as their spring training home from 1933-1958.

“We’re very pleased and encouraged by the effort being put forward,” said Red Sox chief operating officer Mike Dee yesterday, “and we expect to be engaged in serious dialogue in the coming weeks.”

Tentative plans calls for the construction of a new ballpark that will offer about 10,000 seats and room for another 2,000 in an unreserved seating berm.

The team’s player-development complex for minor-leaguers would be housed at the current Ed Smith Stadium, which, until recently, was the spring home of the Cincinnati Reds.

The Sox have an escape clause from their lease at City of Palms ballpark after the 2009 Grapefruit League season, but likely wouldn’t move to Sarasota until February 2011.

The team has been waiting for a counterproposal from Lee County, which governs their current spring training home in Fort Myers, but none has been forthcoming.

Next up for Sarasota County officials: a determination of the actual cost of construction — estimated at $60 million to $80 million — and the negotiations for a lease with the Red Sox.

Plans call for the county to fund the project from a special Tourist Development Tax.

smcadam@projo.com