The SPL chiefs believe they have a chance to sign the Brazilian international away from Real Madrid in the coming weeks.
Vinicius Junior has already agreed to a €1 billion, five-year contract with the SPL, which was negotiated 12 months ago.
This agreement remains in place, and the SPL is now exploring the possibility of Real Madrid selling the star with two years left on his contract.
It has been reported that talks over a new deal with Real Madrid have stalled, as the club is unable to meet Vinicius Junior's demands to make him the highest-paid player.
The SPL is prepared to offer €350 million to Real Madrid to convince them to sell Vinicius Junior.
Al-Hilal has been identified as the potential club to take on the Brazilian star.
According to sources, Real Madrid will not allow Vinicius Junior to run down his current contract, regardless of the situation.