West Ham have already had three bids turned down as they attempt to bolster manager David Moyes’ squad during the January transfer window.
The Hammers have had mixed results since Moyes replaced Slaven Bilic on 7 November.
They beat Chelsea and drew with Arsenal, but have lost four times, including at home to fellow strugglers Newcastle.
One player set to leave this month is striker Diafra Sakho.
The 28-year-old was close to joining French club Rennes in the summer and, while he is still highly regarded by some at West Ham, it has been decided he will be allowed to leave if the club receive an acceptable offer.
The Hammers have dropped into the Premier League relegation zone before Tuesday’s game against second-bottom West Brom at the London Stadium.
Moyes has identified the areas he wishes to strengthen but, as yet, the club have been unable to do deals in what has been described as a “difficult market”.
Swansea defender Alfie Mawson, Newcastle midfielder Jonjo Shelvey and Bournemouth midfielder Harry Arter are the latest players to be linked, with Moyes known to be keen to bring in more players with Premier League experience.