The Dutchman may be considering a move to the Middle East in a year’s time.
Van Dijk is out of contract at Anfield at the end of the 2024/2025 season and has not renewed his deal.
Per Marca, the Liverpool captain could even move this summer, but a year’s time is more likely.
He would command a wage that would make him the highest paid defender in the world.
"I am very excited (for the future), especially next season," he said on his future back in May.
"That feeling came a couple of months ago when we turned the page.
"There is still a lot to work on but now we have the full pre-season to work on it and that is the plan.
"What I am hearing is that it is going to be a very intense pre-season with a lot of physical work, a lot of tactical work and trying to get ready for a tough season. That is very exciting.
"Players are leaving, hopefully players can come in for the start of pre-season. Everyone who can come in and improve the football club will help all of us and push us all.
"The focus for next season will be to make sure everyone is ready and can contribute. It doesn't matter how old you are, you have to perform."