The Boston Red Sox want Jason Varitek back.

It might not be as a player, though.

Two days after signing free agent Kelly Shoppach — giving the Red Sox a full complement of three catchers who are expected to be on the major league squad — general manager Ben Cherington said the team is still talking to the captain and longtime backstop about remaining with the ballclub “in some way.”

“We have incredible respect for ‘Tek. I have incredible respect for ‘Tek on a personal level,” Cherington said Thursday on a conference call with reporters to discuss the team’s latest moves. “We, as an organization and ownership, have incredible respect for him and for the contributions he’s made.

“Our hope is that ‘Tek will always be a part of the Red Sox in some way.”

Cherington would not elaborate on private discussions with Varitek and his agent, Scott Boras, but said they are working to “figure out what’s best for the Red Sox, and what’s best for him.” It has been long assumed that when Varitek is done playing he would join the Boston coaching staff.

But Boras indicated Varitek might not be ready to retire.

“I’ve had discussions with them about ‘Tek, but it’s been about playing,” Boras said. “Any thoughts about coaching have not been addressed, to my knowledge.”

In Providence, R.I., on Thursday, Red Sox owner John Henry said he had tried to contact Varitek to let him know the team appreciates his 15-year career.

Varitek, who will be 40 by the home opener, joined a franchise that hadn’t won a World Series in almost eight decades and became a pivotal part of two championship teams. To Red Sox fans, the turning point was July 24, 2004, when Varitek shoved his glove in Alex Rodriguez’s face during a brawl with the Yankees at Fenway Park — a picture that is as popular in Boston TV rooms as Bobby Orr’s game-winner in the 1970 Stanley Cup finals.

The Red Sox came back to win the game 11-10, then came back from a three-game deficit against New York in the AL championship series en route to their first title in 86 years. Varitek, who became a free agent after that season, re-signed with the team after a protracted negotiation and was given a uniform with a “C” on its chest, making him the team’s first captain since Jim Rice.

The Red Sox won the Series again in ’07 with another solid year from Varitek, but it would be his last. Since then, he has batted .218, including a .220 average last year while appearing in just 68 games.

More disturbing, the captain was not able to maintain cohesion in a clubhouse that disintegrated down the stretch, when the Red Sox blew a nine-game lead in the AL wild-card race and missed the playoffs by one game — the biggest September collapse in baseball history.

With Jarrod Saltalamacchia tabbed as the starter and prospect Ryan Lavarnway looking to move up to the majors this year, Boston signed Shoppach, a product of the Red Sox system, to a one-year, $1.35-million contract this week.

Shoppach, 31, batted .176 with 11 homers and 22 RBIs in 87 games last season with Tampa Bay while throwing out 36.6 percent of runners attempting to steal.

“We know Shop well,” Cherington said, noting that defense was one of the team’s needs. “We felt like in a perfect world, we would look to solidify the catching position by adding strengths.”

Saltalamacchia, who will turn 27 next year, batted .235 with 16 homers in 103 games last year for the Red Sox. Lavarnway hit .290 with 32 homers and 93 RBIs in Double- and Triple-A last year, while also batting .231 in 17 games in Boston in August and September.