The Saudis have offered Fernandes a contract worth £200m to quit Old Trafford this summer.
The Daily Mail says Al-Hilal are willing to table a bid of £100m to United for the midfielder.
Fernandes, via his agents, has also been offered a three-year deal worth £700,000-a-week and up to £65m-a-year in add-ons is on the table.
Al-Hilal want Fernandes to accept the proposal by the end of May as they want the Portugal international to be part of their Club World Cup campaign.
"If the club thinks it's time to part ways because they want to do some cashing in or whatever, it is what it is," said Fernandes after this week's Europa League final defeat.
"In the day that the club thinks that I'm too much or it's time to part ways, football is like this, you never know it. But I've always said it and I keep my word in the same way."