The former Chelsea attacker, now at Lille, is interested in returning to the Premier League, and the Hammers boss has revealed the club are actively pursuing a deal
The 27-year-old left the Premier League after transferring from Chelsea to Ligue 1 side Lille last summer, but has admitted he is "attracted" to the possibility of a return to the English top flight.
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"I think that, as far as I know, the West Ham 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's with us or whoever, we're having a look at it.
"Obviously from his record at Chelsea and his goalscoring record last season in France, and his age, he's very appealing to us."
Allardyce did acknowledge any deal could be scuppered by the Kalou's preference to play centrally, with West Ham already possessing Andy Carroll, Ricardo Vaz Te and Modibo Maiga.
"What regular position he wants to play may be the stumbling block," Allardyce added.