Why not, the Mariners were at their best when they had a quality manager. I'm not sure what Baker could do if he took the job, or why he would even want to deal with the Mariner's front office, but I can't think of a better candidate on the market right now. Though I think it's more likely that the M's promote Daren Brown back to manager (and I don't think that'll happen).
I figured this name would get brought up.
The two issues I see are
1. In 2003, after Lou left and Baker was out in San Fran, Baker was interested in coming here. The interest wasn't mutual however as I don't think he ever was interviewed and we ended going with Bob Melvin and Baker went to the Cubs. If Chuck/Howie weren't interested then, I don't see why they would be interested now.
2. I'm not sure he would be a great fit with the ball club we have now. He has a reputation for being able to handle young pitchers well (Kerry Wood, Mark Prior) in Chicago. That however is just heresay but if that's the case then I don't know if he would be a good fit here.
Think Baker is out of their price range. The guy has had success in the past and isn't going to settle for the league minimum as they like to hand out.
Felix's arm is getting up there but even throwing extra innings I don't think it would do more damage with how he has turned himself into a pitcher not just a hard thrower with great stuff.