The Twins already signed right-handers Ricky Nolasco and Phil Hughes to the two largest free-agent contracts in franchise history last week, but Ryan believes there's still plenty of work to do to improve a team that lost 96 games for a second straight year.
"We want to get good in 2014," Ryan said. "This isn't a mulligan year. We aren't going through any of these meetings and the process and signing Nolasco and Hughes for a mulligan in 2014. We're looking for pieces to make us better. Nobody in Minnesota wants to hear about us getting better in 2015 or 2016, and neither do I."
The Twins remain in the market for a starting pitcher, and Arroyo could be their next target. The veteran right-hander confirmed to MLB.com that the Twins, Angels and Phillies have showed interest.
But the Twins have not made Arroyo an offer yet, and it's unclear if they are willing to sign another pitcher to another multiyear deal after inking Nolasco to a four-year deal and Hughes to a three-year deal. Arroyo, who turns 37 in February, is reportedly looking for a three-year deal.
Ryan, though, said he has payroll flexibility to go after a starting pitcher or even a position player, but didn't get into specifics. The club currently has roughly $75 million to $80 million in payroll commitments next season.
"If somebody makes sense, we'll pursue it," Ryan said. "But if somebody makes sense position-wise, we'd pursue that just as aggressively. I'm not particular here. We have quite a few things we have to address."
Catching remains an issue for the Twins after permanently moving Joe Mauer to first base, but Ryan admitted the market dried up quickly. Minnesota targeted both A.J. Pierzynski and Jarrod Saltalamacchia but fell short of signing either. As a result, Ryan hinted the Twins might have to look to a trade to find a catcher, if they believe rookie Josmil Pinto isn't ready to take over full-time duty.
"It's a little thin, but we're certainly keeping an eye on it," Ryan said. "Whether somebody has someone to free up behind the plate, we need to pay attention to that."
But one area the Twins won't be addressing is the bullpen, which was perhaps the club's greatest strength in 2013. Ryan said he remains more focused on upgrading the rotation than adding a reliever.
"We're not all that aggressive in the bullpen ranks right now," Ryan said. "We're looking at the rotation."
Ryan also noted the Twins will not be taking a pick in Thursday's Rule 5 Draft because the 40-man roster is currently full. It comes as a surprise, as the Twins have put a lot of value in the process over the years, landing players such as Shane Mack, Johan Santana, Scott Diamond and Ryan Pressly via Rule 5 picks.
"We're at 40 and I don't anticipate taking a guy off," Ryan said. "I cannot remember the last time we didn't have the roster at 39. This year, we did quite a bit of work on that Rule 5, but it just didn't work out."