The current Spurs coach only succeeded Andre Villas-Boas in December, and penned an 18 month deal to stay at White Hart Lane shortly after.
However despite enjoying an initial flurry of good results, Levy has been unimpressed with the club’s recent form.
The North Londoners were thrashed 5-1 at home by Manchester City last week and dropped points away to newly promoted Hull on Saturday, frustrating their chairman.
Levy is rumoured to have never seen Sherwood as a long-term solution, and is already lining up Van Gaal.
The experienced Dutchman was linked with the role when AVB was dismissed.
However, his desire to maintain his role as Holland’s coach ahead of the World Cup saw him quickly ruled out if the running.
Levy is hopeful that once the showpiece tournament is over Van Gaal will be willing to step into the Spurs dugout.
Sherwood is likely to be offered a coaching role if this happens, but it remains unclear as to whether or not he will accept such a position.