Gallagher was one of Crystal Palace’s top performances last season, but he returned to Chelsea this summer after his loan term expired.
Since returning to Chelsea, the England international has failed to impress, and he was recently sent off in the Blues’ win against Leicester.
According to The Times, Crystal Palace has made a £27 million approach for the Chelsea midfielder.
With the World Cup approaching, Gallagher needs to ensure he is at the top of his game if he wants to convince Gareth Southgate to select him in his squad.
The report claims that Newcastle and Everton are also interested in Gallagher, but Palace will be hoping they can convince him to return to the club.