To this point they've turned teams away looking to talk trade, according to a tweet from Jon Heyman of CBSSports. However, that could certainly change in the weeks and months ahead.
Two years ago, ownership would have been run out of Boston if they even thought about dealing Ellsbury. Few players produced on the level he did in 2011, as he hit .321 with 32 home runs 105 RBI and 39 steals to finish second in AL MVP voting to Justin Verlander.
At 27 years old, it appeared he was ready to take his place among the game's superstars. However, that changed last season when a shoulder injury cost him all but 74 games, and he hit just .271 with four home runs and 26 RBI over 303 at bats.
That was not the first time Ellsbury missed significant time due to injury, as he was limited to just 18 games in 2010 after breaking four ribs in a collision with Adrian Beltre and re-injuring himself several times.
On the surface, the 29-year-old could be given the injury prone tag given all of the time he's missed over the past three years.
However, when you consider that he missed time due to a rib injury caused by a collision with a teammate in 2010 and a a shoulder injury caused by a collision with Rays shortstop Reid Brignac while sliding into second base last season, perhaps unlucky may be a better way to classify him.
That said, the shoulder injury should not be overlooked, as he clearly did not have the same pop in his bat last season upon returning. An offseason of rest may be enough to rectify that, but oftentimes shoulder injuries can become a nagging thing throughout a player's career.
So the Red Sox have a few different options to choose from.
They can trade him now while he's healthy to a team who's hoping to get the 2011 version of Ellsbury, giving them time to look for a low-cost replacement for this season before presumably turning the position over to Jackie Bradley sometime next year.
They could hold onto him now and wait to see where the team stands come July, as they've made a number of additions this offseason and do have an outside shot of contending in the AL East if things break right.
Or they could just hold onto Ellsbury and make him a qualifying offer at the end of the season. Assuming he stays healthy, he'd almost certainly turn it down to make a run at a long-term deal, which would give the Red Sox draft-pick compensation from whoever signs him.
With so many center fielders on the market this offseason, a number of teams have already filled their center field needs either through signing free agents (B.J. Upton, Angel Pagan) or making trades (Denard Span, Shin-Soo Choo, Ben Revere).
As a result, the market for Ellsbury right now would likely be limited to just a handful of teams. For that reason, I think the Red Sox's best bet is to hold onto him and reassess the situation come July. There really are no marquee names expected to be available at the deadline at this point, so the Red Sox could more than likely get a better package for him then than they would now.
Granted, that all hinges on his health, but for a Red Sox team heading in a new direction, the risk of waiting until the deadline to trade him for a better package of players is one worth taking.
And who knows, maybe Boston will be right in the thick of things and Ellsbury will be at the center of it all as an MVP candidate once again. That could be enough to make all of this moot and convince the Red Sox to re-sign him.