The 23-year-old midfielder has made just three appearances in the Premier League and has been linked with a move away from Leicester in the winter window.
Newcastle United have been credited with an interest in the midfielder and there is also talk of other Premier League clubs exploring a deal for him.
West Brom are also keen on Choudhury, but the Baggies are reluctant to make a move yet.
It is claimed that Sam Allardyce’s side are not sure they want to use up their last loan spot on the Leicester man.
Allardyce wants to make sure he takes a centre-back and a striker to the Hawthorns in this month’s window.
Leicester are also not sure whether they want to loan the midfielder out in the middle of a congested season.
The 23-year-old has been handed outings in ten games across all competitions by Brendan Rodgers this term, though only three of those appearances have come in the Premier League.