Reports claim the England midfielder has been subjected to abuse from some United fans since it became clear he was hoping to leave the north-east to move closer to his family in Suffolk.
West Ham and Tottenham have both been linked with the former Ipswich player, who signed for Newcastle eight years ago.
The Hammers are reported to be ready to offer £4million for Dyer, but Allardyce insists that is some way short of what would be considered acceptable.
"£4million is too low in today's prices. In today's market, for a player like Kieron Dyer who is 27 years old, a top, top player in the Premier League and an England international. It's a gross under valuation by West Ham," he told Sky Sports.
Allardyce also revealed his intention to sign another player in the "very near future" as he continues his rebuilding at St James' Park.
But chairman Chris Mort has expressed his concern at the effect the abuse directed at Dyer could have on attempts to overhaul the squad.
Dyer was booed during the weekend's friendly win over Juventus and it has been alleged that his house has been targeted by an egg-throwing mob.
And Mort warned: "We have to make all our current players and potential new signings see Newcastle as a great place to live.
"It would be disastrous for this sort of behaviour to be repeated."
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