The Englishman has played only 45 minutes in the Premier League under Brendan Rodgers, being brought on as a substitute on three occasions.
Cole endured a similar fate under the Reds' former manager, Kenny Dalglish, which prompted him to move to Ligue 1 side Lille for a season long-loan in 2011-12.
Allardyce spoke to The Mirror about his surprise at Cole's lack of game time: “You would have thought that Joe would be involved there by now, because of all of Brendan’s [Rodgers'] injury problems and his lack of strength in depth.
“But he doesn’t appear to have managed to be able to do that there.
“Whether we move for him depends on where we are and what we do in the next week or two, particularly with our injury list.
“My chairmen extended as much money as they possibly could in August - and went beyond it.
“Whether they can find any more or not is something I will discuss with them in the near future.
“I think if there is a chance [of bringing Cole back to Upton Park], it would be more on the terms of a loan, than on a permanent deal for the player.”
West Ham already have one player on loan from Liverpool, with the Reds' record signing Andy Carroll having joined the London club for the season.
However, Allardyce is likely to face stiff competition for Cole from QPR manager Harry Redknapp, who has not ruled out a move for the Englishman in January.