Hank Steinbrenner, a son of owner George Steinbrenner, said Friday the club probably will meet soon with Rodriguez and agent Scott Boras.
"The fact of the matter is, obviously we want him to stay," Hank Steinbrenner said. "And I think he wants to stay."
Rodriguez had a major league-best 54 homers and 156 RBIs this season, numbers that likely will earn him a third AL MVP award.
He is guaranteed salaries of $24 million in each of the next three seasons from the Yankees, who receive $21.3 million from Texas as part of the 2004 trade that brought A-Rod to New York. If Rodriguez opts out, the Yankees would lose that subsidy.
New York also could select a manager soon, but Hank Steinbrenner said not to expect an announcement over the weekend. The Yankees interviewed bench coach Don Mattingly, broadcaster Joe Girardi and first-base coach Tony Pena and don't expect to talk to anyone else.
"I can tell you at this point, the family and the baseball people are pretty much in agreement," said Hank Steinbrenner, adding the club hasn't offered the job to anyone. "We're close. Still a few details to work out. Do some more thinking on it. That's about it."
Teams aren't allowed to make major announcements during the World Series, but if New York wanted to do so on an off day, commissioner Bud Selig probably would give his permission.