Luis Castro's side have been linked with Barcelona's Raphinha during the current transfer window, but it is understood that the Saudi Pro League outfit are now looking at alternatives.
According to Football Insider, Antony has emerged as a target, with the Brazil international thought to be available for the right price due to his struggles since arriving at Man United.
The 20-time English champions are also thought to be willing to let Antony leave on loan for the 2024-25 campaign providing that his full salary is covered.
Man United paid in the region of £86m for the Brazilian in the summer of 2022, so they would have to be prepared to accept a huge loss in order to sell him this summer.
Antony 'emerges as transfer target' for Al-Nassr
Antony has only managed 11 goals and five assists in 82 appearances for Man United since his arrival from Ajax.
Last season proved to be a real struggle for the 24-year-old, as he only managed three goals and two assists in 38 appearances in all competitions.
Antony was not in the Brazil squad for the Copa America, so he has been involved in Man United's preparations for the 2024-25 campaign.
As it stands, he is set to be in the squad for Saturday's Community Shield against Manchester City, but there is huge uncertainty when it comes to his long-term future with the 20-time English champions.
Does Antony deserve another season at Man United?
There were some positive signs during the 2022-23 campaign, with Antony managing eight goals in all competitions, but he really struggled last term.
Off-the-field issues contributed to his difficulties, with his former partner Gabriela Cavallin accusing the Brazilian of assaulting her on multiple occasions during their relationship.
Antony was given a leave of absence in the early stages of last season to deal with the situation, and he continues to deny any form of physical violence towards Cavallin.
The forward has not been arrested or charged and continues to work with police in a bid to clear his name.
If a suitable offer does not arrive, then Antony will spend at least another few months at Man United, and if he can start to show the type of form that convinced the Red Devils to sign him, then he could yet turn his career with the 20-time English champions around.