ST. PETERSBURG, Fla. -- Andrew McCutchen has been with the Yankees for almost a month now and it's been just as exciting as he figured when first hearing the San Francisco Giants traded him on Aug. 31.

He'd loved being a contributor to a close-knit ballclub that is headed for October baseball.

He'd loved playing in front of packed houses at Yankee Stadium.

He and his wife love, love, love New York City.

He also loves the Yankees' tradition ... the pinstripes, the championships and being linked to many of the greatest names the game has ever known, the likes of Babe Ruth, Lou Gehrig, Joe DiMaggio, Yogi Berra, Mickey Mantle, Reggie Jackson, Derek Jeter, etc., etc.

"When you hear Yankees ... everyone knows about the Yankees," said McCutchen, who was 1-for-2 with two walks and a hit batter Tuesday night in the Yankees' 9-2 win over the Tampa Bay Rays. "Anyone and everyone.The class here is just different. There's just a different feel that you get when you are on this team. You feel like you're kind of part of that history, and just to be even mentioned in it is quite an honor honestly. I've enjoyed my time here."

The five-time All-Star and former NL MVP could be a short-timer, as he's in the walk year of his six-year, $51.5-million contract, but he's already thinking the Yankees could become a long-term home.

"This is the first year being out of Pittsburgh, so being in San Francisco, I had to tell myself that was a place where I could be beyond this year and I'm thinking the same thing about New York," McCutchen said. "This is the place I could be beyond this year. I'm not sure if it will be. It's a possibility.

"This is definitely not a place where I'm like, 'I don't want to be here.' This is a great organization."

A report this week by Nick Cafardo of the Boston Glove this week stated the Yankees would like to re-sign McCutchen as a free agent in the offseason if the cost is "reasonable."

What will McCutchen be looking for?

"It's way too early," he said.

Will the Yankees' be McCutchen's first choice?

"It's too early to say what's a first choice," he said.

McCutchen will be 32 in October and he's no longer putting up the superstar numbers that he did for a few years in Pittsburgh, but his 20 homers, .367 on-base percentage and .793 OPS are impressive.

As a Yankee, he played well enough filling in for Aaron Judge in right field for 2 1/2 weeks that he became the starter in left field for slumping long-time starter Brett Gardner when Judge returned to the lineup on Sept. 18. He's been on base 20 of his 22 Yankees games, and although batting just .233, he has five homers, 21 walks, a .424 on-base percentage and .917 OPS.

As for next season, there are so many unanswered questions before McCutchen has to make a decision.

Will the Yankees do the expected and buy out Gardner for $2 million instead of picking up a $12.5 million club option for 2019?

Will Clint Frazier be over his concussion issues and factor in the Yankees' left field decision?

Will Jacoby Ellsbury, who has two years and $47.28 million to go on his contract, be healthy after missing all of 2018 and be a candidate to start in left or platoon with Frazier?

Will the Yankees try signing free agent Bryce Harper to play left?

"All those things are why I don't think about it now," McCutchen said. "It's too early for me to be even thinking about free agency and where I may be at next year. I can't let my mind go there because then it takes away from the importance of what I'm doing now. There will come a time when baseball's done and I'm actually able to sit down and give it time."

As always, years and money will matter in the winter when McCutchen hits free agency.

At this point, McCutchen has no idea what his value will be in the winter or how the market will play. Will the market be any better than last year when a bunch of free agents didn't sign until after spring training began, current Yankees Neil Walker and Lance Lynn included.

"I don't know, man," McCutchen said. "It's out of my control for the most part. We'll see what happens. I try not to think about it to that extent. I'm just, 'OK, whatever happens ..."

Randy Miller may be reached at rmiller@njadvancemedia.com. Follow him on Twitter @RandyJMiller. Find NJ.com on Facebook.