The Brazilian told Paris Saint-Germain he wanted to leave the club last week.
He asked his management to find him a new club, sparking interest from teams across Europe.
Al-Hilal seized on the opportunity and are now in advanced talks with Neymar, reports Fabrizio Romano.
Paperwork will be sent to Neymar’s camp and it will be up to the player to decide whether he wants to join.
Barcelona were hopeful of re-signing the 31-year-old, who left the Nou Camp for PSG in a world record deal in 2017.
Neymar is understood to be keen on returning to Barca but the Spanish giants may be unwilling or unable to afford his £70million price tag.
It could lead to a loan switch to Nou Camp if his wage payments are shared.
Chelsea have also been linked to Neymar with reports claiming the club was in contact with the player’s representatives this week.
However, conflicting claims suggest that Mauricio Pochettino does not want a reunion with the man he worked with at PSG as he prefers to sign young talent rather than older superstars.
Al-Hilal have deep pockets despite already splashing a reported £150m this summer on Kalidou Koulibaly, Ruben Neves, Sergej Milinkovic-Savic and Malcolm.
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