It's claimed that both teams have made approaches to sign Docherty, with a loan until the end of the season being targeted.
Millwall allegedly have some interest in Docherty, but it's thought that Charlton and Sunderland are the only sides to have made firm approaches.
That may leave Sunderland trailing in the race for Docherty's signature, as Charlton can offer him the Championship football he is looking for, rather than heading to League One again.
Charlton have just lost loanee Conor Gallagher to Swansea City, and that may open up a midfield spot for Docherty to head to The Valley and play regular first-team football.
It's clear that Docherty won't be playing for Rangers in the second half of the season, so heading back down to England on loan could be ideal for the 23-year-old.
Ex-Rangers teammate Kyle Lafferty could always try and tempt him into joining him at Sunderland, but Championship football at Charlton could just win the race.
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