In an email to WEEI earlier today, Cherington called the report from Danny Knobler to that effect "innacurate" and suggesting the Sox were simply doing their due diligence:
Some teams have checked in on him. We haven't told any teams we plan to trade him. It's our job to listen if teams have interest. He's swinging the bat well since coming off the DL and [is] a big part of our team and lineup.
-Via Alex Speier
One of the teams that seems to have "checked in" is the Los Angeles Dodgers. Knobler has noted that the team has scouted Youkilis in their quest to add a hitter to their first-place NL West roster. While Youkilis' contract has often been cited as an impediment, Knobler suggests that money won't be an issue for the new LA ownership. Ken Gurnick of MLB.com, however, disagrees, suggesting that their interest is only "lukewarm" and that they don't want to pay his salary or give up a top prospect.
For now, the Sox will just hope he keeps hitting--be it to help the Sox or build value.