Daily Mail reckons the club have been knocked back in their attempts to strengthen their defence.
Montpellier have rejected the Hammers advances for left back Henri Bedimo, reportedly rejecting a £1.75million bid.
Bedimo is a 28-year-old Cameroon international, and is also capable of playing in midfield.
Allardyce has made no secret of his desire to strengthen during this window, with the defence thought to be the priority.
Bedimo’s experience and versatility has interested Allardyce, although it remains to be seen if the former Bolton Wanderers manager will return with an improved offer.
This window seems to be just as much about which players Allardyce can hold on to, rather than those he brings in, with the likes of Alou Diarra and Mohamed Diame both linked with moves away from Upton Park.
Diame is the one Allardyce is particularly desperate to hold on to, with the Senegalese midfielder putting in a series of commanding displays in the middle of the park during the club’s first season back in the top flight.
West Ham fans were delighted to hear the midfielder reveal he was ‘happy at the club’ last week, as reported by Metro.