Think you're being just a tad disingenuous.
There's probably two sets of people here: i) those who want him gone, as 'he's going away' and ii) those who want him gone, as they keep harping on about this spectacular fall from 3rd. The recent results have been extremely disappointing, so I don't follow that my observation is a strawman at all.
There's also an awful lot of assumption and presumption involved here, namely that: i) the FA actually want to offer Harry the job, and ii) that Harry himself would take it. The truth behind neither is known, merely conjecture. It's speculation and that is all, yet why would you sack a manager purely because speculation surrounds him?
I actually take it as something of a complement, that Harry is linked with other jobs. It says to me, that he must be doing a pretty damn good job; after all, brick managers don't tend to be linked with high profile jobs. And he has done a good job; form is temporary, class is permanent - and the fact remains, that Harry's record in charge of Tottenham is right up there with the best of them.
If the FA want Harry Redknapp to manage England, then why make that task easier for them? If some are to say that the speculation has been such that it has derailed our season - an allegation I'm sure you'll recognise - then should it not be, that we seek to recover substantial 'compensation' in-lieu of the Champions League? That would seem a wiser course of action to me, than merely sacking Harry Redknapp - especially at this stage of the season.