Ryan wouldn't talk specifics about the offer, but according to multiple reports, it's expected to be in the three-year, $24 million range.
Ryan said there's still no timetable for when Cuddyer will make a decision, but that he hopes a decision comes sooner rather than later.
"There will be finality eventually," Ryan said. "I'm not sure how close we are to that point."
Ryan added that the Twins have the advantage of being the only team Cuddyer has ever known, as he was drafted by the club in 1997 and made his debut in Minnesota in '01.
"The situation with Michael is that there's a relationship," Ryan said. "We know him, and he knows us. We know his agent, he knows us. There's not a whole lot of educational process in this. He's known us for years. He's played for the manager and knows the community. There isn't any mystery here, and that's a good thing. But I guess the bad thing is that we're coming off a tough year."
As Ryan noted, the Twins are coming off a 99-loss season that saw them finish with the worst record in the American League. Cuddyer, who is a career .338 hitter in 22 postseason games, would like to play for a winning team, and known suitors include perennial contenders such as the Phillies and Red Sox.
So Ryan said there's still no guarantee that Cuddyer will be back in a Twins uniform next year despite Tuesday's formal offer.
"We're chasing Michael Cuddyer," Ryan said. "If we don't get Michael, we have to make alternative plans. I didn't think there's any hidden agenda here. We'd like to have Michael, but if we don't get him and he goes elsewhere, we'll move on and do something else."
Other options for the Twins if Cuddyer signs with another club, include fellow free-agent outfielders Jason Kubel and Josh Willingham. The Twins already met with Kubel's agent in Dallas, and are tentatively scheduled to meet with Willingham's agent later this week.
Cuddyer also had a busy day on Tuesday, as his wife, Claudia, gave birth to twin daughters, Chloe and Madeline. Ryan indicated it could be a reason why Cuddyer hasn't made a decision yet on his future.
"Everybody has responsibility in that area," Ryan said. "For those of us married, when your wife is pregnant and is about to have twins, your mind is on something other than baseball."