It’s understood Accies price the 21-year-old at £1million plus add-ons.
Cardiff City also are considering Docherty, who has come during the adolescence ranks at New Douglas Park.
Rangers boss Graeme Murty has already introduced in midfielder Sean Goss on mortgage from QPR and Jamie Murphy in a identical deal from Brighton.
Meanwhile, Murty believes the selection of most sensible avid gamers willing to signal for Rangers proves that the membership stays a big attract European soccer.
Scotland striker Stevie Naismith is determined to go back to Ibrox, however Murty admitted he has a number of objectives.
He stated: “We are running laborious at the back of the scenes on various issues.
“You fail to remember the regard the membership is held in round England and Europe, as a result of one of the most people who find themselves phoning up are prime stage.
“It has been nice for me to have a sounding board in Mark Allen [director of football] to lead me in some regards and get me prepped for a hectic length.
“The concept is to make stronger the gang and take us to the next stage than we’re these days working on.”
There may well be avid gamers leaving the membership to make manner for extra new arrivals at Ibrox this month.