With James Collins out with a hamstring injury, Tomkins, Guy Demel and Winston Reid are the only front-line defenders available for Wednesday night's FA Cup third-round replay at Manchester United.
Tomkins has been linked with a move to the Magpies, but Allardyce is keen to add to his defence, rather than weaken it.
"It's impossible," the Hammers boss said. "I might have a problem keeping him if they bid £15million."
Allardyce's defensive options are such that he is hamstrung for Old Trafford, the first of four matches still to play this month, meaning squad rotation is a must.
"There's nobody else I can play," he said.
"There are some players in front of that who play regularly who I will change."
Carlton Cole is poised to start up front, where resources are also limited with Andy Carroll (knee) out and Marouane Chamakh ineligible due to the terms of his loan from Arsenal, while Allardyce is still assessing the best way to integrate Wellington Paulista.
Ricardo Vaz Te could be pushed further forward, with the Hammers potentially changing formation for the fixture.
The manager added: "I'm going to look at the squad, the system. I might tinkle with the system."
With one point from the last five Premier League matches away from home, the Hammers' form on the road is also troubling Allardyce ahead of the trip to Old Trafford. They have scored just five times away from Upton Park this term in the league.
"Away from home we haven't been very good recently," he said.
"The trouble is we don't score. It's that simple. Five goals. It's not good enough.
"You don't need to look any farther than that. Because that puts your defenders under too much pressure.
"Then they make a mistake, and you end up losing a game you should have got something out of.
"You've got to put your chances away, and away from home we're not."
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