The Senegalese only joined the Hammers during the summer but he has been linked with a January departure after it was revealed a clause in his contract could allow him to leave for just £3.5m.
Arsenal have had a disappointing first half of the season and are sixth in the Premier League table, 21 points behind leaders Manchester United and six points off fourth-place Spurs.
So Gunners manager Arsene Wenger is expected to reinforce his squad during the transfer window, with a move for Diame suggested.
But Allardyce said: "You are always worried about losing players but we have not had a bid from Arsenal for Mo Diame. I can't see where he would fit into their side."
Allardyce is also hoping to bring in more new players during January, with Blackburn left-back Martin Olsson on his list.
But after an initial enquiry, Allardyce revealed: "We have not made any further bids for Martin Olsson."