The Ghana international has been linked with a loan move to Upton Park as Allardyce attempts to add some firepower to his struggling side.
The London club have scored only 14 goals in 17 Premier League matches and are languishing just a point above the Premier League relegation zone.
Andy Carroll has not played this season following his move from Liverpool and Ravel Morrison is West Ham's leading scorer with five goals in all competitions.
Allardyce has made no secret of his desire to bolster his strikeforce next month and admitted former Sunderland striker Gyan could be a target.
He said: "We'll be linked with anybody that's a centre-forward that might be coming back into the country,
"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."
Gyan has scored 14 goals in 11 appearance for Al Ain in the Arabian Gulf League this season.
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