ARLINGTON, Texas — A projected future Hall of Famer was keeping tabs on A’s rookie third baseman Matt Chapman during the final series of the season.

Texas All-Star Adrian Beltre told The Chronicle that he’s impressed with what Chapman has been doing since he came up in June; among other things, Chapman batted .389 against the Rangers this year.

“I’m a fan,” Beltre said. “He looks like a really good player. He’s young, but he has a really good glove and bat.

“When I was that age, I wasn’t that good. I had the potential, and I worked hard and developed into a good player. But this guy is good from the get-go.”

For Chapman, who grew up in Orange County as a Dodgers and Angels fan and has watched Beltre since he was with the Dodgers, this assessment was hard to fathom.

“I’m pretty sure he was on his third or fourth season in the big leagues when he was my age, but to hear him say that about me, someone I look up to like that, is amazing,” said Chapman, 24. “He’s been in the big leagues for 19 years; that’s almost my whole life. To hear that is pretty special because I love the way he plays. I still don’t know if I believe him.”

Beltre was in the Rangers’ lineup Sunday after missing four games with a hamstring strain,

“Being in the same game, it’s a little bit different,” Chapman said. “I can remember times I’ve been watching him at the plate and I have to remind myself, ‘I have to get ready to play defense’ almost.”

Beltre believes Chapman — who already is at or near the top of most defensive metrics for third basemen — only will improve.

“It’s all about instincts, and things get easier as you learn the baserunners and learn to anticipate things, you learn when you can take your time,” Beltre said. “The first couple of years will be a test. That’s the time to find more consistency, but he’s going to be very good.”

Chapman drove in Oakland’s first run Sunday with a third-inning double and he finished the season with a six-game hitting streak during which he batted .318.

Susan Slusser is a San Francisco Chronicle staff writer.

Leading off

In closing: Blake Treinen earned his 16th save in 21 chances Sunday and he was unscored upon in his final 10 games, solidifying his hold on the closer spot going into next season. He put up a 2.13 ERA after coming from Washington in the Sean Doolittle/Ryan Madson deal.

— Susan Slusser