Are you sure he can resign just like that?
I don't have the details of his contract, but I assume it's a more or less general football contract he has, which would mean he would have to pay damages to Liverpool (most likely an amount equal to the remaining amount he was to be paid if he continued the job).
That's how it usually goes at least:
- Club fires you, they need to pay out the remainder of the contract (unless both parties agree to a different solution, for instance when the fired one has found a new club)
or
- You resign, you need to pay up because you don't live up to the contract you signed. Usually it's not the manager himself that pays, but rather the new club he's going to. Essentially, if we want Benitez, we need to "buy" his current contract from Liverpool, unless all parties agree to a different solution.