The Yankees first offered Girardi a reported three year deal worth $4-5 million per year on Oct. 4, nearly a week ago. He has still given no indication about whether he would accept the contract as Girardi remains torn between the team he has spent the last six years managing and his hometown Chicago Cubs.
"My guess is it's going to be done one way or another relatively shortly," Steinbrenner said in an appearance on ESPN New York 98.7 FM Tuesday. "Quite frankly, we're going to be starting our baseball meetings soon and we want the manager, whoever that is, hopefully Joe, to be a part of that."
The Cubs have held a strong interest in Girardi since firing manager Dale Sveum after the end of their season.
Girardi is still under contract with the Yankees through October and has not been given permission to talk to Chicago, however.
If Girardi decides he would like to see what the Cubs can offer, that could spell the end of his tenure in New York. The Yankees do not want to go into next month with an unresolved manager situation and would likely begin looking at outside candidates if Girardi rebuffs the current offer on the table.
Girardi has managed the Yankees to a 564-408 record and one World Series title over the last six years.