It's no secret that the Blue Jays were openly shopping Lyle Overbay over the winter, with the first baseman's name popping up in a number of potential deals. He was rumored to be going to the Mets, then to the Mariners, and actually looked to be on the move to Arizona before the Jays called off a proposed Overbay-for-Chris Snyder trade due to worries over Snyder's injury history. Opening Day has come and gone and Overbay is still Toronto's first baseman, but there's no doubt the Jays would move Overbay if a good offer came along.
Overbay quietly posted a solid .265/.372/.466 line in 500 plate appearances last season, with that total largely due to a .905 OPS against right-handed pitching (his OPS against southpaws was just .534). The Jays have been playing Overbay every day, but it's very likely that a trade partner would be looking at Overbay for a platoon or pinch-hitting role given his large career splits --- an .844 OPS against righties and a .702 OPS against lefties.
Toronto can afford to be patient with any deal since top prospect Brett Wallace is waiting in the wings at Triple-A and the Blue Jays don't want to start his arbitration clock until it's necessary. It's also likely that the Jays will have to eat a piece of Overbay's $7MM salary for the season in any deal anyway, so it's not like they'll be saving much money if they trade him sooner rather than later. Overbay's contract is up after 2010, so a new team would likely be looking at him as just a rental over this season's home stretch.
New York, Seattle and Arizona can be counted out of the Overbay sweepstakes due to their acquisitions of Mike Jacobs, Casey Kotchman and Adam LaRoche, respectively. There's also another left-handed hitting first baseman who is both available and provides considerably more power than Overbay: Carlos Delgado. He would be a more expensive option than Overbay, so perhaps a team that doesn't want to meet Delgado's price might look to Toronto as a backup plan.