The fracture in Byron Buxton's left hand is gradually disappearing. The gap between Buxton and the Twins on a long-term contract isn't so easily healed.

The Platinum Glove center fielder rejected a contract offer from the Twins this weekend, a major league source confirmed Sunday, and the team turned down a counteroffer from Buxton's agent, leaving further negotiations for this winter.

But the chasm between Buxton's potential payday as a free agent, and the Twins' desire to protect themselves financially if he continues to play less than half the team's games, might have more immediate consequences with the MLB trade deadline looming Friday. If the Twins believe Buxton won't be in the Twin Cities beyond the 2022 season, when he becomes eligible for free agency, they might be more inclined to trade off major parts of the team now and undertake a multiyear rebuilding project.

Players under team control beyond this season — Jose Berrios chief among them, but also including veterans such as Kenta Maeda, Taylor Rogers, Josh Donaldson, Max Kepler or Jorge Polanco — could be marketed to teams this week or this winter, in hopes of stockpiling young prospects for a future rebuilt contender.

And Buxton? It's difficult to imagine either side backing down, given the enormous disparity between what he is worth when he plays — as one of the most valuable players in the major leagues, he could be worth tens of millions of dollars per season — and the difficulty he has had staying healthy. Buxton, who missed his 73rd game of the 2021 season Sunday, has played only 321 of the Twins' 646 games over the past five seasons, slightly less than half. His current stay in the injured list is the 11th of his career.

Buxton, like Berrios, has said he would like to remain with the Twins. But with only 15 months remaining until the other 29 teams can enter the bidding, it appears increasingly impossible to find a contract structure that both sides could agree to.

"Every player has to do what that player thinks is right, and these types of conversations are difficult for a lot of guys. I know they were for me," Twins manager Rocco Baldelli said Sunday, though he was not speaking specifically of Buxton. "I turned down a contract [during] my second year in the big leagues, and never ended up making up the dollars or years on a deal at any point going forward."

The MLB trade deadline is 3 p.m. Friday, and the Twins, who already dealt Nelson Cruz on Thursday to Tampa Bay for a pair of Class AAA pitching prospects, are expected to be busy. Whether they plan to keep the team together and try to contend next season should be far more obvious once that deadline passes.

"Getting on the other side of this week always gives every team some clarity about what the final couple of months of the season will look like," Baldelli said.

Perhaps the next few years, too.

Luis Arraez "is having trouble running," Baldelli said, leaving the Twins no choice but to place him on the injured list. "If he was able to run and we felt we could get him back out there today, we would have probably left him active and just worked through it. But it didn't look like he was progressing much."

Arraez has a strained right knee after falling while trying to field a line drive in Chicago on Tuesday.

Arraez's absence meant Jake Cave played for the first time in 74 days, since the Twins discovered his sore back was the result of a fractured disc. Cave beat out an infield hit, reached on an error and struck out twice Sunday.

Staff writer La Velle E. Neal III contributed to this report.