The Netherlands boss will be out of work following the World Cup in Brazil, having decided not to extend his contract with the Dutch national team.
He has confessed his desire to test himself in the Premier League and been linked heavily with Tottenham, who are reportedly expected to oust Tim Sherwood from the dugout at the end of the season.
Levy could return for the 62-year-old after the World Cup, but The Mirror reports that he will have to compete with Spartak for the former Bayern Munich manager's signature.
They claim that Moscow will apparently try to tempt Van Gaal into joining them with a lucrative offer and that Spurs would pull out of an auction for his services with them or Manchester United.
Van Gaal has also been touted for the United post if they decide to part with David Moyes.