Dembele scored his 17th goal of the season as the Bhoys beat Aberdeen 3-0 to secure the Scottish League Cup on Sunday and is already attracting interest from a string of top European sides, according to reports.
Celtic's Patrick Roberts, Moussa Dembele and Erik Sviatchenko celebrate winning the Scottish League Cup
West Ham's need, however, is arguably more pressing, with summer signings Simone Zaza and Jonathan Calleri struggling to impress for Slaven Bilic's side, who currently sit a point above the relegation places.
According to the Sunday People, Bilic is "on the lookout for a new striker as he battles to save his job", with Inter Milan's Stevan Jovetic and Juventus' Mario Mandzukic both on his list of targets, along with Dembele.
West Ham United boss Slaven Bilic
And the Hammers boss could make a move in January, depending on whether he is backed or sacked by London Stadium chiefs David Gold and David Sullivan.
Dembele only arrived at Celtic Park in a cut-price deal from Fulham in July, but would almost certainly command a Scottish record transfer fee.
Victor Wanyama is the current most expensive Premiership export, having left Celtic for Southampton in a £12.5 million deal in 2013.
The Saints - who also paid £11.5 million for Virgil van Dijk and £10 million for Fraser Forster, both ex-Bhoys - were themselves added to the list of Dembele admirers last week (ESPN).
Southampton's ex-Celtic pair Virgil van Dijk and Fraser Forster