Ryan, who officially replaced Bill Smith on Monday, said he had a "nice conversation" with Cuddyer earlier this week, and said the Twins should have room in the budget to make a fair offer to Cuddyer.
"We can usually find a way to make that work," Ryan said when reached by telephone on Thursday.
Twins owner Jim Pohlad also didn't rule out Cuddyer's return when asked about the possibility at Monday's press conference re-introducing Ryan as interim GM.
"I love Michael Cuddyer, but we want to win, so if Terry convinces us that he's part of that, and we can win, then he'll be back," Pohlad said. "Assuming Michael agrees with it. I love the guy, my wife loves the guy. He's a great player, we wouldn't want him to leave. He's a great part of the organization. But the first goal is to win."
There's certainly no guarantee Cuddyer will return, however, as he met with Phillies officials at a meet-and-greet on Tuesday at Citizens Bank Park. Cuddyer is said to be looking for at least a three-year deal, and the Twins don't appear likely to get into a bidding war to retain his services.
But the Twins have the advantage of being the only organization he's ever known, as he was drafted by the club in 1997.
Cuddyer even said at the end of the season that the idea of staying with the same team for his entire career would be a factor in his decision.
"I think so, yeah," Cuddyer said on the last day of the season. "It's very rare for that to happen. To have a 'legacy,' in this organization is important. So it's something that will definitely go into the thought process."
The Twins are hopeful they can use that to their benefit. Cuddyer fits plenty of needs for a club because of his power from the right side, his versatility and his leadership in the clubhouse.
"He's everything we believe in here," Ryan said. "He's a good player, he fits, he's a right-handed bat, a good community guy. All the things that make the Twins who they are over the years, I think Michael possesses."
Ryan also made sure to point out the Twins plan on getting back to their winning ways next season, and that he doesn't view next year as a rebuilding year despite losing 99 games in 2011.
"We're going to try to win," Ryan said. "There's no question about that. We have some good players here and hopefully over the winter we have our guys report to Spring Training without any of their ailments. So there's no reason to think we won't go through this thing without trying to win."
Cuddyer, though, said at the end of the year that he didn't need to be convinced the Twins were going to be a winning team next season in order to re-sign with the club.
"I don't think it's fair ... to throw it all on them, and tell them they need to do, 'This, this and this in order for me to consider coming back,'" Cuddyer said. "If I'm going to come back, then I'm one of those pieces. So I don't think it's fair to throw that on the organization."
But Cuddyer wasn't the only Twins free agent Ryan reached out to this week, as he said that he also called Jason Kubel, Joe Nathan and Matt Capps.
"I wanted to follow up with those four particularly because they're free agents," Ryan said. "All of them were very complimentary and appreciated the call. They've earned that right to be free agents. I'm sure they're hearing from other clubs but that's the process we're in right now."