Allardyce has made no secret of his desire to strengthen West Ham's squad during the January transfer window, but the 59-year-old has so far missed out on all of his targets.
West Ham have struggled with numerous injuries recently and have been dragged into a relegation battle, but Allardyce looks set to miss out on Vermaelen as he seeks to bolster his options.
He acknowledged that Arsenal manager Arsene Wenger will be keen to hold on to the centre-back, with their London rivals fighting on several fronts.
He said: "I think under the circumstances at Arsenal with the situation they're in with the Champions League and cup matches, they've had to use him as soon as any of the two defenders are injured.
"I don't think there's any chance we'll get someone of his quality, but it would be nice if we could.
"I'll keep going and hope we get some (new players).
"We had a terrible day (on Saturday) when we thought a player was going to sign for us and then I found out he wasn't, but there you go."
Allardyce also highlighted the importance of getting his numerous injured stars back playing, with the former Bolton boss adamant they will play an integral role in helping them avoid the drop.
He added: "(Andy Carroll's) had a long gruelling rehab programme but I think having Andy, Kev (Kevin Nolan), Ravel (Morrison), Guy (Demel), Joey (O'Brien), George (McCartney), Winston (Reid) back as soon as possible is critical for us.
"It's critical in the fact that without these players we see what results we are getting.
"If we're going to get out of it, these players have to get back and stay fit. If additions can come in (they will help). We're finding (that) very difficult to achieve."
Finally, the manager confirmed reports that Lacina Traore would not be arriving on loan from Monaco, with Everton said to have recorded a late interest in the Ivory Coast international forward.
"It's unlikely (that he will join West Ham) by the sounds of it," he said. "(Any other club) can apply for a work permit like we did.
"They would have to do a separate application."
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