Roy Hodgson has stated he is keen to bring in a number of new faces this month in his first opportunity to add to his squad since taking charge in September.
Reports in Italy have now claimed Babacar is a target and the 24-year-old is likely to be open to a move away from La Viola in the winter window.
The 24-year-old one-cap Senegal international scored 10 goals in 22 Serie A appearances last season, just 13 of which came as starts, but this year he has been unable to secure regular game time.
Babacar hasn't started in the Italian top flight this season although has still managed four goals in 15 appearances as a substitute.
Senegal have qualified for the World Cup and it is thought Babacar is looking for a move away from Fiorentina to try and force his way into his country's squad for the tournament in Russia.