Dan Haren is a favorite of executives, but his back issues make it unlikely that he'll receive a contract offer of more than two years.
Most teams would prefer a one-year contract with an option year.
"I would guess the free agent player who is having his medical records gone through with a fine-tooth comb more than anyone out there is Haren," said an American League executive.
"You love his past durability, but now you have to be careful that he actually missed a few starts last season. He's one of those guys you'd love to add to your rotation."