The Tottenham midfielder joined Gers on-loan in January to the end of the season.
After victory over Aberdeen on Saturday, Rohl was asked about Rangers fans wanting Moore to stay: "Yeah, me as well. There’s no question. I think conversations are always there (with Tottenham), but we know when Mikey performs like this, you can see he enjoys playing for Rangers.
"The fans love him, I like him, he’s a key player. I think there’s a lot of good things where we could go again together. We know he’s still not our player, let’s work in the next couple of weeks in all those directions (to bring him back).
"Since I came to the club, Mikey is getting better and better. We started this week to prepare for the summer. I think we are in a good position, we are very clear what we want.
"I think it’s also helpful now that we have the idea of how I want to play football, committed with a fantastic owner, with the good people around me — everything goes in the right direction.
"We work hard, we have again a good summer that we prepare for next season, but let’s finish this season strong and successful. The most important thing is that we bring good results in the next seven games. If we win the next seven games, we will win the league."