Dyer was arguably Newcastle's best player when he came on as a second-half substitute against Juventus and, although many fans would be delighted to see the back of him, we all know how good a player he can be.
Allardyce is a brave man to knock back £5m, and he must be confident West Ham will go higher.
The one thing Sam has in his favour is that Manchester City and Tottenham Hotspur are also said to be in the running. But, as yet, neither club has put cash on the table. But obviously it is a gamble Newcastle are prepared to take.
West Ham's Alan Curbishley did not seem very enthusiastic last week when asked about his interest in Dyer, but then again, he wouldn't be ... would he?
Supposedly Dyer has revealed a determination not to allow his critics to break his spirit, but now that his home and car have been attacked by Toon fans, personally I'd "get the hell out of Dodge" as soon as I could.
The abuse directed at him on Sunday appeared to motivate him, rather than dishearten, as he guided a young side through the final 45 minutes of the friendly. But the pitch is the safest place he has to hide these days.
West Ham Offer For Dyer 'Knocked Back'!
Have the Mags and Hammers reached deadlock in their negotiations? Will Spurs or City come forward with an offer?
Allardyce revealed on Sunday that nobody had made a bid that is "anywhere near the sort of money" he is looking for. And if an auction takes place he will come away with great credit if he ups the money received. But Dyer has a shocking injury record, and any deal is sure to include add-ons for appearances.
There is the chance Dyer could go out on loan, as we reported yesterday, but Newcastle are unlikely to be happy with that option because his market value will fall as he only has two years left on his contract.