It has been reported that Rangers have opened talks with Hamilton over a £600,000 deal for the Scotland Under-21 international.
The Daily Record has claimed that Cardiff City in the Championship in England are also interested in the 21-year-old, but the youngster would prefer a switch to the Ibrox club.
Rangers have made two signings already in the January transfer window. The Scottish Premiership club have signed winger Jamie Murphy and midfielder Sean Goss on loan from Brighton and Hove Albion and Queens Park Rangers respectively.
Docherty is a hugely talented midfielder, and the Scottish Premiership midfielder would be a good signing for Rangers, not just for now but also in the long run.