"There were several organizations that showed some interest," Baker said. "I'm sure some were just kicking the tires, and some were very serious, and the Cubs were very serious.
"The organization, obviously, it's kind of in a rebuilding mode, but that's not necessarily a bad thing in my opinion. We were just looking for a nice fit."
According to a report in the Minneapolis Star Tribune, the sticking point was the Twins wanted an option for 2014, while Baker wanted a one-year deal to reestablish his value for next offseason because he's coming off elbow surgery.
"The reaction we have is that obviously it wasn't meant to be," Twins general manager Terry Ryan said.
But Ryan didn't want to get into specifics about what the Twins were looking for in terms of a new contract with Baker.
"It doesn't matter," Ryan said. "He decided to sign with the Cubs and we wish him well. There's no sense getting into anything deeper than that. Given the right situation, we would've liked him back but he chose the Cubs. So we wish him well."
Baker, 31, had spent his entire career with the Twins, posting a 4.15 ERA in parts of seven seasons with the club. He struck out 770 and walked just 224 in 958 innings.
He leaves Minnesota among the club's all-time leaders in several categories, including starts (11th with 159), wins (11th with 63) and strikeouts (11th).
Baker was the club's Opening Day starter in 2010, but his best season came in '11, when he posted a career-low 3.14 ERA. But he was limited by elbow problems in the second half of the season and ended up throwing just 134 2/3 innings.
Baker entered Spring Training in '12 saying those elbow problems were behind him only to have those issues resurface before the start of the season.
The Twins announced he'd have season-ending surgery to clean up scar tissue on his flexor pronator muscle on April 17, but once the surgery started, Dr. David Altchek decided that Baker also needed to have his ulnar collateral ligament repaired.
Baker said at the end of the season that his rehab was going well and that he hoped to be ready for the start of the 2013 season.
He was an intriguing option for the pitching-starved Twins, but ultimately the club will have to go another route. Only left-hander Scott Diamond is guaranteed a spot in the rotation next season.