According to Nick Cafardo, the contract talks seem to be progressing:
4. Josh Beckett, RHP, Red Sox—One major league source indicated that there’s more optimism about the Sox and Beckett reaching a contract accord this season. It seems talks have been amicable, if not productive. The Sox could insist on medical language similar to what’s included in the deals of John Lackey and J.D. Drew. Jason Bay wouldn’t bite on the language, but Beckett may consider it just to stay in Boston, where he has already forged a great relationship with Lackey and continues to build one with Jon Lester.
Sox fans, before you get excited about the prospect of keeping Beckett around long-term, remember this: Beckett has previously said that he does not want to negotiate during the season, so if the Sox and Beckett are going to come to terms on a new deal, then it will have to happen in the next three weeks.
That's not an impossible task, but I have my doubts that the Red Sox and Beckett will come to terms before the season begins.