"I have a list. The Yankees are on the list," Soriano said before the Cubs played the Arizona Diamondbacks. "I talked to my family and my family supports me in any kind of decision that I make. It's good to hear that from my family, especially from my wife. My wife said any decision you make I will support."
Epstein said Soriano asked for two or three days to think about his decision.
"I know he made some comments to you guys, but there won't be any official notice to the club before tomorrow at the earliest as to whether he will except a trade or not," Epstein said.
"He asked us for a couple of days. He will let us know where he will go, if anywhere. At that point it will be up to us if we want to move forward with finalizing a deal."
Soriano said Epstein told him other teams were interested in the outfielder, but he believes there is a "good chance" he could be dealt to the Yankees.
Soriano, 37, began his career with the Yankees and would have some familiar faces waiting for him if he returns to the Bronx.
"It was great when I used to be with the Yankees," Soriano said. "My best friend with the team is [Derek] Jeter and he's still there. Mariano [Rivera] is still there too. And me and [Robinson] Cano are good friends, too, because we're from the same town. I could feel very good with the Yankees because I've been part of the family before with them."
Soriano has $25 million left on an eight-year, $136 million contract that expires after the 2014 season. He's batting .254 with 17 home runs and 51 RBIs this season and has heated up in July, batting .299 with eight home runs and 16 RBIs. He's 11 hits shy of 2,000 for his career and 11 home runs short of 400.
Soriano said this is as close as he's ever been to a trade from the Cubs, and he said he looks forward to another chance at a World Series.
"I wanted to stay here for the rest of my contract, but at the same time I want another chance to get into the playoffs and the World Series," Soriano said. "I would have been very happy if we were playing better here with a chance to go to the playoffs, but it's not. I am 37, so I'd like one more chance to go to the World Series. They're preparing to win in 2015, and that's too late for me. I've tried to be a champion here, but now it seems I have to do that for another team."
Soriano, who was out of the starting lineup for Wednesday night's game, said he will be patient as the Cubs try to make a deal.
"There's no rush right now," he said. "There's six or seven days left [until the July 31 trade deadline], so they want to make sure they get the best offer and that's OK with me."