Ryan wouldn't confirm that he already has offers on the table for starting pitching, but the club made offers to free-agent pitchers such as Joe Saunders and Francisco Liriano, according to reports.
The Twins also have been linked to free-agent starters such as Brett Myers, Kevin Correia, John Lannan, Brandon McCarthy, Ryan Dempster and Mike Pelfrey. They also inquired about Rangers left-hander Derek Holland, according to a FOX Sports report.
But they saw one potential option sign elsewhere, as Joe Blanton agreed to a two-year deal worth $15 million with the Angels. Ryan, though, said there are still plenty of candidates out there.
"We've had more discussions," Ryan said. "We've had more dialogue. We've had more exchanges with various guys. But whether or not it comes to the finality of bringing a guy in we'll see."
Ryan added that payroll isn't an issue for the club, as it currently sits at about $70 million after opening last season with a payroll around $100 million. He said it could be around that $100 million mark like last year, but it depends on the situation.
"It's fluid," Ryan said. "I don't have any problems with where we're at."
But Ryan all but ruled out adding a high-priced starter such as Greinke or Sanchez, as he doesn't want to tie up too much salary to only a small group of players. The Twins are already set to pay Joe Mauer and Justin Morneau a combined $37 million.
"I think it's dangerous to start putting such a high percentage of your payroll on just three or four guys on a team," Ryan said. "It just doesn't work. I think it's a recipe for disaster. When you've got 50 or 60 percent wrapped up in three or four guys, historically that hasn't worked, and I don't think it'll ever work."
The Twins also remain in the market for a third baseman to create competition for Trevor Plouffe. But St. Paul native Jack Hannahan doesn't appear to be a fit, as he's been offered a Major League deal from at least one other club while the Twins are only offering a Minor League deal, according to a source.
Hannahan wants the chance for regular playing time with a Major League contract and has garnered interest from seven clubs, including the Twins, Yankees, White Sox and Reds.