The Hammers are keen to bring the Ivorian back to the Premier League after he impressed for Lille last season in France.
The versatile 27 year old has a £2.8million buy-out clause in his current contract and has admitted that he wants to return to England.
West Ham want the former Chelsea man to use either out wide or down the middle if and when summer signing Andy Carroll gets injured.
West Brom are also interested in signing Kalou and have also been in contact with the players agent but Allardyce is confident the East London club can get a deal done.
“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.”
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