Manchester United are prepared to give Athletico Madrid star a huge pay rise so they could sign him this summer.
United sent scouts to watch Saul as he helped knock Liverpool out of the Champions League last month.
He would fit the profile that United boss Ole Gunnar Solskjaer is seeking as he continues to rebuild the side.
Saul put pen to paper on a long deal with Atletico back in 2017 that runs through until 2026.
Saul has scored four times in 37 appearances for Atletico this season, including the only goal of their Champions League last-16 first-leg tie against Liverpool in Madrid.
They subsequently won 3-2 at Anfield after extra time to secure their place in the quarter-finals if and when the season resumes following the coronavirus pandemic.