Conte, who won the Premier League with Chelsea and also managed Tottenham Hotspur in England, was responding to speculation that he had requested full control while also making financial demands of the struggling Old Trafford club.
United sit 13th in the Premier League and 20th in the Champions League standings following Wednesday's humiliating 4-1 thrashing by Italian side Como, increasing scrutiny on Carrick.
"My name has been linked with numerous clubs, but there are currently no negotiations at an advanced stage," Conte said in a statement.
"Following a wonderful and successful spell in charge of Napoli, I will take the time I need to consider how and when to return to management," he added of his time in Naples where he won Serie A in the 2024-25 season.
"It will be a carefully considered decision, one I will make when I believe the conditions are right.
"I have read reports of financial demands and requests for full control that I have supposedly already made to the clubs mentioned, as well as reservations about what has been described as my 'strong personality'.
"These reports are unfounded, as there is currently no concrete basis for such assessments."
Concrete opportunity
Conte, who last coached Napoli in the 2025-26 season, said that if a concrete opportunity arose, he would enter talks with the club involved and "jointly consider the terms of a potential agreement", taking into account the needs of both parties.
"Until then, any assumptions about my demands and my professional future remain speculation and cannot be treated as fact," the 57-year-old Italian added.
In an interview with The Athletic earlier this month, Conte said he would like to manage a club that has "lost sight of their history" so he can help "make it shine once more".
Defeat against Como extended United's winless run to seven games in all competitions and skipper Bruno Fernandes said his team had adopted a "mood of defeat" while also questioning the tactics, with Carrick apologising for the performance.
Brighton manager Fabian Huerzeler, another name linked with the United job, also distanced himself from the speculation on Friday.
The 33-year-old, England's youngest top-flight manager, said he was focused solely on Brighton, who sit third in the Premier League after a string of impressive performances.
"I have no time to think about these rumours because we play every three days and, beside that, I have a lot of respect for Michael Carrick and what he has done with Manchester United the last season," Huerzeler told a press conference.
"He's a great human being, a great personality. There's nothing more to say about that."
