Tim Tebow came a lot closer to following in the footsteps of Babe Ruth and Mickey Mantle than we thought ... because Yankees general manager Brian Cashman tells TMZ Sports the team gave real consideration to signing the ex-NFL star.
"We certainly thought a lot about it," Cashman tells TMZ Sports ... "there’s a lot of characteristics about his reputation and character that are really attractive."
In fact, Cashman says the Yanks sent TWO scouts to Tebow's MLB workout in L.A. last month.
Of course, Tebow ended up signing a minor league contract with the NY Mets -- and Cashman says he thinks the guy could have real value as a baseball player down the road.
"He’s a legitimate athlete, no question about it. So you can’t deny there’s potential, something there. But it’s an uphill battle."
Cashman makes it clear he has nothing but respect for Tebow -- but explains why the Yanks ultimately decided he wasn't the right fit for pinstripes.