Murty has already added Sean Goss and Jamie Murphy to his squad this month but remains in the market for further reinforcements before the transfer window closes.
Initial discussions have now taken place with Accies over a potential move for Docherty, who is contracted at the SuperSeal Stadium until 2020.
Murty said: “We had made an approach but that’s as far as things have gone. I have said before I am not willing to talk about players who are at other clubs.
“We are looking to bring others in as we want the group to get stronger and be better. The more good players you have in, the more it pushes others to a higher standard and it’s a challenge for those who are already here.
“From what I have seen the players who are here have responded. There is movement, there is work behind the scenes. The guys back at the training ground are working on bringing people in and improving the squad. We are hopeful we can bring in more players.”
Murty watched his side round off their trip to America with a 4-2 victory over Corinthians at the
Spectrum Stadium yesterday.
Rangers came from two goals down to follow up their win over Atletico Mineiro as Alfredo Morelos netted twice with Andy Halliday and James Tavernier also finding the target.
Murty said: “We did okay in the first half, I was pleased with parts of our possession play. I said to the players at half time that good players will punish mistakes and that’s what happened. We were a little bit slack at times. In the second half we were more forceful and overall it was another worthwhile exercise.
“Anytime a forward gets two goals he’s a happy guy, he got man of the match too, so Alfredo is delighted.
“It’s about pushing the squad and making everyone better and if we can take this attitude back to Glasgow with us it will be good for all of us because in my opinion there is more to come from this group.”