An extension to Joe Mauer, who is scheduled to become a free agent after the 2010 season is deemed a priority for this team. However, the Twins have other players as well who will demand salary raises at this point, because there are arbitration-eligible. Here is a list of the arbitration-eligible and free agents (in parenthesis the money that would be freed by not re-signing them) for the Minnesota Twins after the 2009 and 2010 seasons. With trading season ahead, this might be a core of players around whom the Twins will look to build a trade.
After the 2009 season:
Luis Ayala ($1.3M+)
Joe Crede ($2.3M+)
Mike Redmond ($950K)
Carlos Gomez (super 2)
Glen Perkins (super 2)
After the 2010 season:
Jesse Crain ($1.7M+)
Mike Cuddyer (team option) ($9.4M)
Matt Guerrier ($1.5M+)
Jason Kubel (team option) ($4.1M)
Nick Punto (team option) ($4M)
Additional money that will come off the payroll after the 2009 season is the $2.6M the Twins are paying Mike Lamb. Furthermore, Phillip Humber is paid $1.15M this season (thanks to a major league contract signed by the Mets). Releasing him will alleviate that cost
The source of most information for his was Cot's Baseball Contracts.