Warnock announced his retirement from management in April 2022, ending a 42-year career in which he won a record eight Football League promotions and managed 1,603 matches.
But speculation has mounted in recent days that the 74-year-old, who managed Cardiff between 2016 and 2019 and guided them into the Premier League in 2018, is set to return to the Welsh capital.
Cardiff are currently 20th in the Sky Bet Championship and have gone seven games and two months without tasting victory, raising question marks over Hudson's future.
But Hudson, who succeeded Steve Morison in September and was later told by Cardiff owner Vincent Tan that he would be in charge at least until the end of the season "unless he does badly", says he has been assured that Warnock will not be replacing him.
Speaking before Sunday's FA Cup third-round tie at home to Leeds, Hudson said: "I've spoken to them behind the scenes and it's 100 per cent not true.
"I spoke to the chairman (Mehmet Dalman) and I was told there were rumours. That's part and parcel of football, but 100 per cent it's not Neil Warnock in that respect.
"My job is to concentrate and then look forward to a big game against Wigan.
"I've been in football a long time. Speculation is speculation and it will not deter my focus from what the job is.
"That is something I will continue to do - and that (Warnock rumour) was put to bed.
"I know my job is to get results, regardless of speculation of any situation where we are."
Hudson is currently unable to make any January signings as Cardiff have been placed under a transfer embargo.
FIFA put Cardiff under the embargo over their failure to pay the first instalment of the £15m transfer fee for the late Emiliano Sala to French club Nantes, although Hudson says the club are working to resolve the situation.
Cardiff's build-up for the Leeds cup tie has been disrupted by a virus sweeping through the squad.
Callum Robinson, Gavin Whyte and Cedric Kipre have all been affected, while Kion Etete (hamstring) is also unlikely to be risked on Sunday.
Full-back Mahlon Romeo has been ruled out for at least four weeks with a hamstring injury.
Cardiff have confirmed Sean Morrison is leaving after eight and a half years at the club.
Former captain Morrison made 295 appearances for Cardiff but the 31-year-old central defender has not played since suffering a serious knee injury in February 2022.
Hudson said: "Sean won promotion and player of the season here and created some amazing environments for players in the dressing room.
"He has been so welcoming to everyone around the club and been a huge influence. I want to wish him all the very best going forward."