The Hammers are short in the centre-forward department, having sold Sebastien Haller to Dutch Eredivisie giants Ajax for around £20.25m this month.
Michail Antonio is the only remaining senior striker in David Moyes’ side, but the Englishman has already missed eight league games due to injury this season.
West Ham are looking to add to their strike force during the winter transfer window and has been linked with several players, but are yet to find a solution.
As the London-based club continue to sort their striker situation out, they are willing to give teen talent Odubeko chances in the senior team.
The Irishman made his senior debut for the Irons in their FA Cup tie against Stockport County on Monday, coming on as a late substitute for Antonio.
Odubeko was even considered to start against the Hatters this week and is expected to get more playing time in the coming weeks.
The teenager joined West Ham from Manchester United in 2019 in an attempt to have a better shot at first-team opportunities.
