Alex Bregman has put up staggering numbers at Fenway Park and would appear to be a perfect fit for the Red Sox, who need a right-handed hitter to balance their lineup. Kevin M. Cox/Associated Press

The Red Sox held their first Fenway Fest over the weekend. The one-day gathering in Boston replaced Winter Weekend, an annual tradition for the previous eight years.

Fans met current and former players, posing for pictures and getting autographs. Yet many were thinking about a player who isn’t on the team.

Thoughts of free-agent Alex Bregman, a veteran right-handed hitter who would help balance out the lefty-heavy Red Sox, were palpable at Fenway. As the team was introduced at the MGM Music Hall behind center field, a fan held a sign that said “Make an Offer to Bregman.”

Several Sox players took pictures of the sign. No doubt some sent a copy to Bregman. Not sure if anyone sent it to chief baseball officer Craig Breslow, but there’s no doubt he got the message.

“We talk about balancing out the lineup with a right-handed hitter,” said Breslow, “someone who can take advantage of the dynamics of Fenway Park. That tends to be right-handed hitters who hit the ball in the air to the pull side, you know?”

Bregman has pull power and was able to use the ballpark dimensions in Houston to his advantage. Fenway has been even friendlier to the longtime Astros star, who has an insane 1.240 OPS with seven home runs in 98 plate appearances in Boston.

He has done it as a third baseman, manning the hot corner for 89% of his big-league games. The Sox continue to say Rafael Devers is their third baseman, but manager Alex Cora, who was the Bregman’s bench coach in Houston for two years, said he could see Bregmen playing a different position.

“Alex was a Gold Glover at third base, we all know that,” said Cora. “But in 2017 I had a conversation with him. He needed to play third because it was (Carlos) Correa and (Jose) Altuve. But I always envisioned Alex as a Gold Glove second baseman. His size, the way he moves, it felt like you will be a second baseman but he has played (third base) at a high level.

“We’ll see where he ends up, and where he ends up playing.”

The Red Sox will have to pay a premium to bring Bregman to town. Sources say they have spoken with Bregman’s agent, Scott Boras, but there has been no indication the Sox are anywhere close to a deal.

At Fenway, there was much talk that more than two months remain until the 2025 season begins. That’s a lot of time to improve the roster with right-handed power, whether it’s a free agent like Bregman or a player acquired via trade. Word is the Cardinals are still looking to deal 10-time Gold Glover Nolan Arenado, and he would very much like to come to Boston.

On Saturday, Red Sox president and CEO Sam Kennedy talked about the need to add talent via the free-agent market, but also talked about staying disciplined.

“We’re happy with the offseason in terms of where we are so far,” said Kennedy. “We really are, in terms of our needs. But we’ve still got work to do.”

Sox fans at Fenway Fest, happy to meet the current roster of players, would agree. And many of them knew exactly who they wanted the Red Sox to add before the season begins.

Tom Caron is a studio host for the Red Sox broadcast on NESN.