At $2.1M you probably aren't looking at a new job for a couple hundred K more. If he gets offered $4-5M, then money is probably a big factor. But if he's looking, it's because he wants a different location, different bosses, better facilities, easier recruiting, more authority (perhaps more say in his own staff or less of his bosses looking over his shoulders), closer to home, some other family situation, or to deal with a different fan base or press corps or whatever else I missed. None of that changes by just throwing more money at him. If he deserves more, pay him before that does become a factor. I don't see that he does deserve more though, as junior and skerfan said. If there's other things that can and should be fixed/improved, do it.
Personally, I think $2M is too much for a college coach and $5M is absurd. I understand we have to compete in the market for coaches, but I hope we are never pushing the boundaries.