The team signed pitcher Francisco Liriano earlier this offseason, but has been mostly quiet since suffering another losing season in 2012.
Lohse was expecting a big payday, but has yet to receive a multi-year contract from a team. With Spring Training having started, Lohse might be forced to sign a "pillow contract," which would mean that he would sign a 1-year deal with a club.
The issue with Lohse signing a pillow contract is that the team that signs him will forfeit a first-round draft choice, which many teams are reluctant to do under the new system. The Pirates certainly are not a fit as they are a team rebuilding and accumulating young talent to form a new core.
Lohse declined a qualifying offer from the Cardinals at the beginning of the offseason, but the team is reportedly not interested in bringing the right-handed pitcher back despite the mounting injuries they have seen to their starting pitching.
Lohse would be a good fit for any team looking for roughly a league average starter who can eat innings. It remains to be seen who that team will be.