"The Yankees may walk," one source from outside the organization said.
The Mariners haven't accepted the offer quickly, and there is now a bit of pessimism.
The Mariners and Yankees are in the midst of a four-game series in Seattle. Lee is scheduled to start tonight's game. The 2008 AL Cy Young Award winner owns an 8-3 record this season with a 2.34 ERA.
While the Yankees have been in the mix for Lee for weeks, they were seen as less likely than some others to obtain him since they have said they are happy with their current rotation, which features All-Stars CC Sabathia, Phil Hughes and Andy Pettitte.
The Rays, Twins, Rangers, Phillies, Reds, Red Sox and Mets are among the "12 to 15" teams that have inquired about Lee, whose contract is set to expire at the end of this season. Seattle has been targeting big-time prospects in return, such as Montero, the Rangers' first-base prospect Justin Smoak, the Twins' catching prospect Wilson Ramos and the Rays' young pitcher Wade Davis.
The Mariners aren't believed to like Ramos as much as Montero, as Ramos has had a couple injuries in his career. Montero is only 20 and is seen as a hitting star. But the Yankees have a stockpile of young catchers, with also Austin Romine, Gary Sanchez and Francisco Cervelli.