NEW YORK -- Yankees managing general partner Hal Steinbrenner said that he has had ¡°more than one¡± conversation with Aaron Judge since the end of the club¡¯s postseason run, adding that he considered those talks to have been ¡°very positive.¡±

Steinbrenner spoke to the YES Network¡¯s Meredith Marakovits for an interview that will air in its entirety on Monday evening.

Asked if he feels confident that Judge will remain in pinstripes, Steinbrenner replied: ¡°I have made it clear to him that is our wish. He means a lot to this organization, and I¡¯ve made it clear to him we¡¯re going to do everything we can to make that happen.¡±

Whatever dollar amount Judge ultimately receives, it will be higher than the seven-year, $213.5 million extension that Judge rejected before Opening Day, a move that general manager Brian Cashman has called ¡°the all-time best bet.¡±

Judge responded by setting an American League record with 62 home runs, leading the Majors in numerous offensive categories like runs (133), homers, RBIs (131), on-base percentage (.425), slugging percentage (.686), OPS (1.111), OPS+ (211) and total bases (391).

Cashman said at this week¡¯s GM Meetings in Las Vegas that he has been in contact with Judge¡¯s agent, Page Odle. Yankees manager Aaron Boone said he has exchanged a couple of text messages with the slugger since season¡¯s end and remains hopeful for his return.

¡°First and foremost, I love the person,¡± Boone said. ¡°To get to be alongside him for five years now and watch him become the player, leader, person, husband and everything -- it¡¯s been fun to watch him and see how he¡¯s evolved and learned how to really continue to get better as a Major League player.¡±

Though Judge struggled during the postseason, batting .139 (5-for-36) while hearing boos at Yankee Stadium during the Astros¡¯ American League Championship Series sweep, Boone said he does not believe fan reaction will influence Judge¡¯s decision.

¡°Look, he¡¯s beloved here,¡± Boone said. ¡°He knows that. He loves it here. I think he loves the fan base. He¡¯s one of those guys that truly isn¡¯t affected by that and understands there¡¯s going to be moments in time that literally everyone probably experiences at some point if you wear this uniform long enough, even if you¡¯re great.¡±

As of 5 p.m. ET on Thursday, Judge can speak freely with representatives from any team. The Giants are one potential suitor, and while not speaking about Judge specifically, San Francisco president of baseball operations Farhan Zaidi said this week that ¡°from a financial standpoint, there¡¯s nobody that would be out of our capability to meet what we expect the contract demands will be.¡±

¡°So then,¡± Zaidi continued, ¡°it will just be a question of whether there¡¯s mutual interest and how we put together the best possible team.¡±

Though there could be a geographic component to a potential Giants offer for Judge, who grew up about 100 miles from San Francisco in Linden, Calif., and attended Fresno State University, Judge has repeatedly said that his preference would be to remain in New York with the Yankees.

¡°I always go back to my teammates,¡± Judge said this week on MLB Network. ¡°Those were the guys that ride or die with me the whole season. Those are the guys who really pushed me day in and day out to go out there and be my best. I definitely wouldn¡¯t have been in this position or had the season I did if it wasn¡¯t for those guys.¡±