The Hammers boss saw James Collins suffer a hamstring injury during Saturday's 3-0 defeat at Sunderland and is already without the services of George McCartney and Joey O'Brien, with the duo on the treatment table.
Tomkins has been linked with a move to Newcastle, with the Magpies battling to retain the services of Fabricio Coloccini, but Allardyce would be loath to lose another member of his squad.
Teenage defender Dan Potts made his Premier League debut in the setback on Wearside, with the youngster culpable for Sunderland's second goal, when his hesitation allowed Adam Johnson to score.
Allardyce said: "We have never been in a position to sell anybody and we don't want to. We want to increase the size of the squad, not decrease it and sell anybody.
"It was less likely James was going to leave in the first place, even less likely now.
"Now we only have two centre-halves left, James and Winston Reid, and we have a 19-year-old at full-back because we have no-one else, so I need two in if I am honest.
"I have been looking for a left-back for the last 10 days."
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