The Ghana international has been linked with a loan move to Upton Park as Allardyce attempts to add some firepower to his struggling side, who have scored just 14 goals in 17 Premier League matches.
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"We'll be linked with anybody that's a centre-forward that might be coming back into the country," said the West Ham boss ahead of the side's Boxing Day clash with Arsenal.
"If there's a player of any sort of quality we try and find out what the situation might be - but it is nothing more than that."
Allardyce was also questioned about defender James Tomkins, who had been charged with assaulting a police officer, and revealed that the 24-year-old has not broken any club rules.
"From a legal point of view it's difficult for me to comment," Allardyce continued.
"The only thing I can say is that I don't think James should have been there irrespective of whether he got into trouble or not.
"It's probably the highest profile public house in this country and I think it would have been better if he'd have stayed away.
"From a club point of view there's nothing broken in terms of rules because it was five or six days ahead of the next game. I can't comment any further than that."