Despite Spurs sitting just four points adrift of Premier League leaders Chelsea, Nuno remains under pressure to keep the club in the top six.
According to The Athletic, Levy has demanded that sixth position is a minimum requirement if the Portuguese is to retain his job on a long-term basis.
The report says that Levy included a clause in Nuno's two-year contract which permits a departure in 2022 without the head coach being due any compensation.
Nuno was only appointed as the permanent replacement to Jose Mourinho after Levy had tried and failed to secure the services of multiple other candidates.
In total, Nuno has recorded six wins and four defeats from his opening 12 matches in charge of the North London outfit. body check tags ::