Stoke City midfielder Joe Allen is the latest player to be linked with a January move to West Ham.
The Daily Mirror say Hammers boss David Moyes is keen to sign the former Liverpool man when the transfer window reopens.
Moyes is said to want Allen because the player can operate as a defensive midfielder or further forward.
Meanwhile, according to The Independent, West Ham are competing with Stoke, Newcastle and West Brom to sign striker Danny Ings on loan from Liverpool.
West Ham will not sell Reece Oxford and are keen on former Chelsea man André Schürrle, according to The Guardian.
Youngster Oxford has been recalled from a loan spell at Borussia Mönchengladbach amid reports that he could be sold by the Hammers.
RB Leipzig, who initially tried to sign him last year, have reportedly expressed an interest in signing him.
Leipzig were reportedly confident that an initial offer of £8m, rising to a potential £17m with add-ons, would convince West Ham to sell.
However, The Guardian say West Ham have decided against allowing Oxford to leave during next month’s transfer window and that he has been recalled because Moyes has decided to exercise a clause in the loan deal enabling him to take Oxford back to the London Stadium.
The Guardian also say Moyes is interested in signing Germany international forward Schürrle on loan from Borussia Dortmund.
Schürrle, 27, made 44 Premier League appearances during an 18-month spell at Chelsea, scoring 11 goals before being sold to Wolfsburg in 2015.
Moyes recently confirmed his interest in signing Sevilla’s former Stoke and Blackburn midfielder Steven N’Zonzi.
Swansea’s former Brentford centre-back Alfie Mawson is also said to be a Hammers target.