Waghorn looks a safe bet to be fit in time for the trip to Celtic Park on September 10 after initially being ruled out for two to three weeks following a scan last Tuesday.
Warburton said: “Waggy has made great progress, and credit to him and the medical team. He is out jogging and they will gradually increase the loading. We won’t welcome him back too soon but he is certainly way ahead of the curve.”
The Ibrox boss added: “Jason Holt will have another appointment this week. He has an ongoing ankle problem which hopefully can be resolved fairly quickly and that is why he wasn’t involved on Saturday.
“Jason had an operation previously on the ankle and he rolled it in training. We hoped it would have resolved itself but then he had some discomfort.
“He is too important to risk, and players’ welfare is a key aspect to us so we will get him looked at and make sure he is okay. Hopefully we can welcome him back very shortly.”
Matt Crooks started full training on Monday as he bids to make his debut following ankle surgery, while Josh Windass is close to rejoining his team-mates following a nerve problem.