One of those is rumoured to be former Chelsea and Tottenham head coach Conte, who was reported to have already held talks with United having been out of work since leaving Napoli in June.
Target: Antonio Conte has been heavily linked with the Manchester United job
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However, the Italian has now taken to social media to address such speculation, insisting that he is not in “advanced negotiations” with any club and hitting out at what he called “unfounded” reports over his financial demands and concerns over his “strong personality”.
Conte posted on his Instagram Story: "Following recent media reports in Italy and abroad, I feel it is appropriate to clarify my position.
"My name has been linked with numerous clubs, but there are currently no negotiations at an advanced stage. 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. 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.
"Should a concrete opportunity arise, that will be the time to hold discussions with the club concerned and jointly consider the terms of a potential agreement, with due regard for both parties’ needs and the qualities and approach that define my work as a manager.
No interest: Fabian Hurzeler looks set to remain at Brighton
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"Until then, any assumptions about my demands and my professional future remain speculation and cannot be treated as fact."
Another prominent target linked with the position at United is Hurzeler, who has in-form Brighton flying high once again in the Premier League this term.
However, it has been reported that the German has no interest in the job at this stage, with The Telegraph claiming that United would have to pay a world-record fee for a manager to get him out of a contract at the Amex Stadium that contains no release clause.
Asked about those United links ahead of Brighton’s Premier League trip to Liverpool this weekend, Hurzeler said: “I'm really focused on my job here.
“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.
“He's a great human being, a great personality. There's nothing more to say about that.”