He has rejected offers for Modric from Real Madrid - the latest being £30million plus £8m in add-ons, says the Daily Mail.
Levy has set a £40m asking price and will not accept a penny under that mark, while the Spurs supremo is also unhappy with the structure of Madrid's previous offer.
Discussions between both clubs are on-going but the Spanish side are currently unwilling to budge on their latest bid, placing considerable doubt over the transfer given Levy's tough stance.
Spurs' resolve to recoup £40million for a player they signed for £16.5million from Dinamo Zagreb four years ago has been strengthened by Modric's recent training boycott.
The Croat failed to turn up to two pre-season training sessions and also skipped the club's tour of the US, infuriating the Tottenham hierarchy in the process.