Yankees owner Hal Steinbrenner says he's open to expanding Alex Rodriguez's role with the team and praises him for how well he works with the young players. (0:40)

TAMPA, Fla. -- Yankees owner Hal Steinbrenner can envision Alex Rodriguez's role with the team growing over time.

"Absolutely," Steinbrenner said Wednesday afternoon, surrounded by nearly three dozen media members in the corridor of the spring training stadium that bears his father's name. "We haven't talked about that. Obviously he's been doing some broadcasting as well and he's got other things going on in his life. But, look, the more he's involved, he's actually tremendous with the young players. Always has been. We are going to continue talking about different ways he can be involved."

Rodriguez, currently a special adviser to the owner, is expected for one or two stints as an instructor during spring training. It is common for former Yankee great to be involved in spring training. The likes of Reggie Jackson, Goose Gossage and Ron Guidry are constant presences at the training facility. What is different is that those former greats are not being paid $21 million by the team. The Yankees, who cut A-Rod as a player last August, still owe him as the terms of his 10-year, $275 million contract.

Steinbrenner said he did not have specifics about how Rodriguez's role could grow. A-Rod has said he doesn't plan on ever managing, but has expressed a desire to be an owner. A-Rod's career earnings as a player are $441,285,104, according to Baseball-Reference.com.

Meanwhile, Steinbrenner wouldn't say if manager Joe Girardi would return in 2018, but he made it clear that he admires Girardi's work. Girardi -- who has only guided the Yankees to one playoff game since 2012 -- is in the final season of his four-year, $16 million contract.

"We love Joe," Steinbrenner said. "Joe is one of many people who work in this organization that have contracts. I treat all of them the same. I don't deal with it until the contract is up."

Steinbrenner said the criteria he uses to judge a manager includes being able to work with both young players and veterans, being smart and the ability to handle New York. He said Girardi does all three.

"He has done a good job," Steinbrenner said. "We have to see how this year goes."