The news outlet reports that Gallagher is currently weighing up his options, with several clubs interested in taking him on loan for the rest of the season
The Chelsea youngster has been one of the standout players in the Sky Bet Championship since moving to Charlton on-loan, and his performances have led to interest from a number of clubs in the second tier, as well as some Premier League clubs.
Reports even suggest that Scottish Premier League side Rangers are interested in bringing the 19-year-old midfielder in on loan, should he decide to leave Charlton.
Burnley and Norwich City are the Premier League sides in question, with West Brom, who are chasing promotion back to the top flight also reportedly interested.
Football London reports that Gallagher has settled in brilliantly at the Valley and is enjoying playing under Lee Bowyer, which has caused him to be undecided whether or not to leave the club.
It has been a difficult season for Charlton Athletic. After a strong start to the season, injuries have cost them, and the Addicks now find themselves 19th in the Sky Bet Championship table, just five points above the relegation zone.
For Lee Bowyer, survival is the main target in their first season back in the second tier, and Conor Gallagher remaining at the club could be crucial to that, with the midfielder having netted six goals in the league so far this season.