Amare was unhappy in Phoenix because he felt he was being de-emphasized for an aging, declining Shaq. In Minnesota, he'd be the clear first option, the feature big man. In addition and perhaps more important, no team could offer him as much as Minnesota could.
People talk about how players want to bolt small cities and such, but ultimately money talks. Precious few big-time free agents leave the team that holds their Bird rights, assuming that team wants to retain them. And it's purely because the NBA makes bidding wars impossible and the most money is always at home (again, for max deal players that the team wants to keep).
And as a "soft" factor, if Minnesota really does trade Love for the #2 pick and selects Rubio, you have to think Amare would like to play with a potentially elite fast-break and pick-and-roll point guard.
There's a chance Minnesota could lose him, but I'd place the chance of that very, very low.