The Foxes have turned down a £9m offer from Crystal Palace for Jeffrey Schlupp
Schlupp was not selected by Avram Grant for the 2017 Africa Cup of Nations in Gabon due to lack of much game time at Leicester City this season.
He has expressed his interest to continue his career elsewhere, but his coach Claudio Ranieri is still holding on to the 24-year-old.
Allardyce replaced Alan Pardew last month after the club let him go due to the dreadful start he oversaw this season, but things have been just as bad under the former England boss.
He is expected to return with a fresh bid, but will face major competition from West Brom's Tony Pulis, who is very keen on signing the 24-year-old. Pulis wants to bring Schlupp in to provide cover, as well as competition, for James McClean and Allan Nyom.