It has being reported in certain quarters that Warne, contracted to the club until June 2023, will be offered a new deal in the event of the Millers making it a hat-trick of promotions straight back to the Championship under his watch.
The Millers, who have won their last League One games without so much as conceding a goal, are 11 points clear of third-placed MK Dons heading into Friday night's top-of-the-table home game with nearest rivals Wigan Athletic.
Warne, who last signed his current deal with the club in the autumn of 2020, said: "I'd be lying if I did not think about my family's security, but the article is categorically untrue.
"No-one at the football club has said anything about a contract or anything, so it isn't true.
"I have spoken to a player that I am trying to get to extend and they asked me about my future and I was a bit like: 'well, I just go game by game really.'
"It is something I have thoughts on, as all my staff do. Obviously, they all have. (But) It is difficult in football, as one minute you can be reasonably secure like 'Johnno' (Lee Johnson) my mate at Sunderland who won manager of the month (in December) and then he is sacked (in January). It is difficult, but I cannot say I lie awake in panic.
"I feel that we have done a good job here and it's been a really enjoyable job. But we have probably done enough to get a job somewhere else if we do 'get the bullet'. So I do not lie there panicking about it like I possibly did in years gone by."