The 24-year-old has been frozen out of the first-team picture under head coach Jose Mourinho and former Spurs boss Mauricio Pochettino is keen to reunite with Alli in France.
Sources have told ESPN that Alli is keen on the move and Mourinho is willing to let him go but Levy is proving to be the major stumbling block.
Alli was a key part of the Spurs team which reached the 2019 Champions League final and has been one of the club's most successful acquisitions having been signed for just £5 million from MK Dons in February 2015.
He has since gone on to make over 200 appearances but has started just six times this season with Mourinho questioning his work ethic and publicly labelling him "lazy" in the recent Amazon "All or Nothing: Tottenham Hotspur" documentary.
Sources have told ESPN Alli is desperate for first-team football, not least because he faces a fight to hold down a place in Gareth Southgate's England squad for the delayed Euro 2020 finals this summer.
Sources added that PSG have shown a willingness to negotiate regarding the possibility of inserting an option to buy in any agreement and are willing to offer a loan fee but Levy is yet to give them a final answer despite being aware of their interest for some time.
Levy notoriously does late business in transfer windows but PSG are pushing for an answer ahead of Monday's 11 p.m. GMT deadline.