Warburton was appointed the Rangers manager in the summer of 2015 and has a contract until June 2018.
The former Brentford boss has done a remarkable job at Ibrox so far, with the Gers likely to get automatic promotion to the Scottish Premiership at the end of the 2015-16 campaign.
Rangers are at the top of the Scottish Championship table at the moment with 69 points from 27 matches, 14 points clear of second-placed Hibernian.
According to The Scottish Sun, Championship outfit Derby County have Warburton on their radar.
Rangers assistant manager Weir, though, has made it clear to the fans that the Englishman is not going to leave the Gers at the end of the season.
“Mark is not one for throwing about glib comments,” Weir told The Scottish Sun. “He says what he means. We are 100 per cent focused on this.
“It’s a great job, a big job and we’re loving it. We’re working towards something here and Mark realises the potential, he’s an intelligent man.
“We haven’t had any talks or any thoughts about going elsewhere. I can assure you we are enjoying the job here.”
Rangers will return to action on Saturday afternoon when they take on Scottish Premiership outfit Dundee at Ibrox in Glasgow in the quarter-finals of the Scottish Cup.