The 27-year-old, who scored 15 goals in France after leaving Stamford Bridge for free last summer, is thought to want to start down the middle, and that is something West Ham may not be able to offer.
"As far as I know, back at West Ham, I think the chairman is speaking with the player's agent," Allardyce told Sky Sports News.
"We understand the player wants to come back and play in England, whether that is with us or with whoever, we are having a look at it.
"Obviously from his record at Chelsea, and his goalscoring record this season in France, and his age, he is very appealing to us.
"But whether that will come off or not in terms or what regular position he wants to play, may be the stumbling block."