The Saudi Pro League outfit are said to have made an 'astronomical offer' for the Portugal international in January, but Fernandes made it clear that he would not be interested in making the move to the division at this stage of his career, believing that he still has a lot to achieve in European football.
According to Record, Al-Hilal are refusing to give up on a big-money deal for the 29-year-old and are planning to make another offer at the end of the 2023-24 campaign.
Jorge Jesus's side are top of the Saudi Pro League table, picking up 53 points from their 19 league matches this season, which has left them seven points ahead of second-placed Al-Nassr.
Al-Hilal already have a number of famous players in their squad, having brought in Kalidou Koulibaly, Ruben Neves, Aleksandar Mitrovic, Sergej Milinkovic-Savic, Yassine Bounou, Malcom and Renan Lodi.
Fernandes made the move to Old Trafford from Sporting Lisbon in January 2020, and he has represented Man United on 215 occasions, scoring 71 goals and registering 60 assists in the process.
The Red Devils captain has again been a vital player at club level this season, scoring seven goals and registering seven assists in 31 appearances in all competitions.
Fernandes has a contract with Erik ten Hag's side until the summer of 2026, with the option of a further 12 months, but he could potentially become one of the best-paid players in world football by moving to the Saudi Pro League.
The Portuguese provided an assist in Man United's 3-0 win over West Ham United on Sunday, although he has not scored in the Premier League since the start of November.
Fernandes has only won one trophy during his time at Old Trafford, which proved to be last season's EFL Cup, but he also has runners-up medals in the FA Cup and Europa League.
Man United's only realistic chance of silverware this season comes in the FA Cup, with the team set to take on Bristol City or Nottingham Forest in the fifth round of the competition later this month.
Back-to-back wins over Wolverhampton Wanderers and West Ham have also put Ten Hag's side back in contention for a Champions League position in England's top flight.
Ten Hag's side are now up in sixth position in the Premier League table, six points behind fifth-placed Tottenham Hotspur and eight behind Aston Villa in fourth ahead of next Sunday's trip to Villa Park.