I hope he tells them to feck off after how they acted. There aren't any obvious options out there, unless they bring in an old manager with no great desire to make the job permanent, like Toshack (who is sometimes consulted by Henry), and invite either Gerrard or Danny Murphy to assist as a means of acquiring experience. But that would surely be a lot of disruption for no real purpose. They'd be much better advised to support Rodgers until the summer.
Look at the realistic options among 'resting' managers: Pulis, thank god, wouldn't agree to be a caretaker; Martin Jol, likewise; Chris Hughton, possibly but he's neither a safe pair of hands nor a positive coach; Hoddle - he's re-learnt how to talk a good game but has had minimal impact at QPR; then there are the deadbeats like Curbishley, and the oddballs like Di Canio. Chilling stuff.
Then look at the ex-Reds: Thommo - did okay steadying the ship as caretaker but surely long past consideration; Barnes - after Tranmere surely unemployable; Murphy - keen but completely untested; Bellamy - in some ways he's just what is needed among the current backroom staff (he'd demand greater commitment, and wouldn't be afraid of telling Gerrard to sort himself out), and as he's a Rodgers fan the manager would be wise to consider adding him pronto, but again completely untested as a stand-in boss; Toshack - twice-passed over for the job in the past, now probably content to play a cameo role, but another who is well past his prime; Keegan - well we all know what would happen. Again, a depressing bunch.
Steve Clarke would probably be the least unlikely short term choice, but he wasn't much better organising the defence the last time he was here, and he's not going to lift the mood with the force of his personality.
Rodgers looks better for the short term at least the more you look at the alternatives.