The centre-back was supposedly offered a one-year deal by the Light Blues, but, as he did in the wake of rumours linking Robin van Persie with an Ibrox switch, Warburton has dismissed any talk of a move.
"It's another one we've apparently signed, we've offered him a one-year deal. It's news to me. I'm not amazed it comes out but there's no truth in it," he told the Evening Times.
Celtic manager Brendan Rodgers
Brendan Rodgers has confirmed to the Daily Mail that he would love to get two deals done imminently, with Scott Sinclair seemingly being one of the players he was referring to.
The Hoops have added two players to their squad this summer, but speaking before Sinclair's move stepped up a gear, Rodgers insisted that he would like to double the number of incomings in the coming days.
"Ideally I would hope one of them would be over the line this weekend. If the other one wasn't by Monday then hopefully not long after that," he told the Mail.
Celtic's Scott Allan
The 24-year-old has joined Rotherham United, but Rodgers has insisted that he could still force his way into his plans in the future.
"The opportunity came up for him to go to Rotherham for a manger he knows. We will asses it when he comes back," he told The Scottish Sun.
Rangers manager Mark Warburton
Warburton has asked Rangers' supporters to balance their expectations with an understanding for an effort the squad are putting in to get the club back towards the top, the Evening Times reports.
"We understand them but we hope also they understand the effort going in to take the club back to where it used to be," he told the Evening Times.
The Welshman has claimed that the Gers will be nowhere near the title picture.
"They are not even good enough to finish second or even third in my book," he told The Scottish Sun.
"I've stuck them down for fourth place."
"I asked Nir Bitton already and he said they are a really good side so we need to be ready," he told The Scottish Sun.