The setup man suffered the injury in a March 19 Grapefruit League game while attempting to get out of the way of a well-struck grounder against the Blue Jays.
Timlin played catch at a distance of 90 feet on Monday.
"He probably could have gone to 120," said Francona. "Tentatively, he would be ready for Pawtucket on the 7th and the 9th. I think that's kind of what we're leaning toward doing. Again, there will be some sides and flat work up to that point. But that's the way the schedule plays out. Then, on the 11th, hopefully he'll join us. Some of that is going to depend on how he feels, but that's the schedule we've worked out."
The timing would be perfect, as Timlin has enjoyed success against several of the Yankees' better hitters, including Johnny Damon (.136 average against Timlin), Jason Giambi (.118), Derek Jeter (.269) and Alex Rodriguez (.238).
When Timlin returns, the Red Sox will have a tough roster decision to make. In fact, that will also be the case when Josh Beckett comes off the disabled list on April 6.
Two pitchers will have to go, and the Red Sox have several relievers on the bubble who don't have Minor League options, including Javy Lopez, Kyle Snyder, Bryan Corey and David Aardsma.
"There's guys out there that know we have to make moves and are probably feeling it a little bit anyway," said Francona. "I don't need to add to that. You want your roster to be perfect every day of the year but it probably just isn't realistic. It just doesn't happen. The guys we have, we like. It's not like we're trying to sneak a Rule 5 kid in there. We have veteran guys so we're not going to have that flexibility."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.