Warburton was appointed the Rangers managers at the end of last season and has done a great job at Ibrox.
The 53-year-old’s success at Rangers has not gone unnoticed back in England, with The Scottish Sun claiming that Championship duo Fulham and Queens Park Rangers are interested in his services.
Northern Ireland international midfielder Davis, who joined Southampton in the summer of 2012 after leaving Rangers, hopes that Warburton remains at Ibrox.
“Mark is a talented manager and I am sure there will be interest in him from other clubs,” the 30-year-old told The Scottish Sun.
“But it’s important that Rangers start to build something again and it looks as if Mark and Davie Weir have started to do that.
“They have been excellent since they came in. I’ve seen a few of the Rangers games on the TV and they are playing really good stuff.
“They have made a few good signings and they are looking strong for the title.”
Rangers are in great form at the moment and are on course to winning the Scottish Championship this campaign.
Warburton’s side are at the top of the league table at the moment with 36 points from 13 matches.
Rangers are five points clear of Hibernian, who are currently second in the standings.
The Glasgow outfit will take on Livingston away from home in the Scottish Championship after the two-week international break.