MINNEAPOLIS -- The spacious corner lockers of the Twins’ clubhouse at Target Field are reserved for the four veterans of the highest seniority and stature on the team.

From the corner to the right nearest the door where players crossed the threshold from the baseball world back into the real world, a teary Sonny Gray was one of the last to leave following the Twins’ elimination from the playoffs on Wednesday. He had the best view in the room of the names on the backs of the neat rows of cream jerseys hanging in the lockers -- and, at that moment, those men represented by those jerseys were no longer his teammates.

Gray has waited a long time for his right to test the free-agent market for the first time. But as he reflected on his next steps and the bright future he predicted for that clubhouse, he kept using the words “we” and “our” when referring to the organization.

“I don't know if this is the right thing to say before going to become a free agent,” Gray said. “But I'll say it because it's honest: Money is not the ultimate factor for me. Never has been. Having said that, you want to be valued appropriately.”

It’s bold of him to acknowledge so openly. But clearly, Gray has an idea of what he wants and values in his next destination, forged from more than 10 years of service time in this league across four different organizations. He’s grown from the successes in Oakland, Cincinnati and Minnesota and has undoubtedly learned from the struggles of New York.

Now that Gray and his family have experienced two years here, does Minnesota check all of their boxes?

“It does,” Gray said without hesitation. “We've had an incredible experience here.

“But going into Spring Training this year, [my family] wanted to become a free agent. We wanted to experience that. We wanted to see what it's like. I know how good I am. We want to bet on ourselves, essentially, and I know that I have a whole lot left to give to the baseball world.”

He showed that with a career season as a 33-year-old, pitching to a 2.79 ERA in 32 starts, striking out 183 with an MLB-best 2.83 FIP and 5.3 WAR, per FanGraphs, that ranked fourth-best among all pitchers. He’s likely to be one of the most coveted arms on a free agent market that will be shallow in high-end starting pitchers.

And with Gray, Kenta Maeda and Tyler Mahle all set to hit free agency from the Twins’ crop of starters, there’s room to add to the Minnesota rotation. Pablo López, Joe Ryan, Chris Paddack and Bailey Ober are a solid top four, but the Twins will want additional help to lessen immediate reliance on youngsters like Louie Varland and Simeon Woods Richardson.

But the Twins have never been a team to spend big on free-agent pitchers, as their four-year, $55 million deal with Ervin Santana ahead of the 2015 season remains their largest ever commitment to a pitcher in free agency, and their four-year, $73.5 million extension with Pablo López represents their biggest commitment overall to a pitcher.

There are also real questions of how the Twins’ payroll capacity will be impacted by the expiration this offseason of their TV contract with Diamond Sports Group, the parent company to Bally Sports North.

President of baseball operations Derek Falvey noted that he didn’t expect Gray to make a quick decision considering his market and how long the veteran right-hander has been waiting for this free-agent opportunity.

“We have a ton of respect for him, for his agent and ultimately, we’ll stay in contact with him,” Falvey said. “That process needs to play out to some degree. I’m really proud of what he accomplished over the last couple of years for us. We’ll continue to have dialogue with Sonny, but that process is going to take some time to work through the part of the free agent process that he’s earned.”

But within that context, the Twins’ decision-makers are well-aware of Gray’s affinity for Minnesota -- and of his sentiment that money might not be everything.

“When a guy really does want to say something like that, I think there is a reason for it,” manager Rocco Baldelli said. “He’s not doing it by accident. It’s probably something he really feels. That’s what we really want to hear. He was one of the best pitchers in baseball over the last two years. Of course, we would love to have him back.”

It’s all about family for Gray. He emphasized many times over that he, his wife and children have enjoyed the Twin Cities and being part of the Twins’ organization, which has allowed his two sons, Gunnar and Declan, to enjoy the Twins’ clubhouse environment and the baseball life every step of the way.

Playoff baseball is now what drives Gray as a competitor -- and he made it clear that he feels there’s “something special” to come within the next few years for the Twins.

But he’s also made it clear that he’s been looking forward to his shot at the open market -- and lots will be on his mind this winter.

“We've enjoyed every single moment that we've had since we got traded over here -- not only the people in the clubhouse, the fans, the city, the organization,” Gray said. “Everyone has been as much as you can ask. It's been an incredible experience.

“To be able to come back into the postseason this year and to pitch, to play and to win and do all the things you dream of as a player and all the things that's going to continue to push me moving forward, I do feel like the opportunity is here and it's definitely ahead of us. But I don't know. I don't know where that's going to lie, but you do want to go to a place you feel wanted.”