Alli has been linked with a loan move to the Parc des Princes throughout the January window, which shuts at 11pm on Monday.
The England international has been frozen out at Tottenham by Jose Mourinho this season.
Alli has not started a Premier League game since the opening weekend of the campaign.
Mauricio Pochettino, who was appointed as Thomas Tuchel’s successor as PSG boss last month, is keen to be reunited with Alli in the French capital.
The player himself is also said to be keen on a move as he seeks more regular first-team football ahead of this summer’s European Championship.
And Mourinho is also happy to let Alli leave, having only handed him 75 minutes of Premier League action this term.
However, Alli is still unsure whether he will be permitted to join PSG for the remainder of the season.
According to the Daily Mail, the saga could go right down to the wire as negotiations between the two clubs continue.
Tottenham chairman Daniel Levy has yet to sanction the deal due to concerns over a lack of mdifield cover.
Spurs do not want to let Alli leave unless they can secure a replacement, which looks increasingly unlikely with just hours of the window to go.
Christian Eriksen was a potential target but Inter now look set to keep hold of the former Spurs man.
And with Giovani Lo Celso currently out injured, Alli’s hopes of sealing a switch to PSG are hanging by a thread.
Mourinho’s side were beaten 1-0 by Brighton on Sunday, leaving Spurs six points adrift of the top four.
Chelsea visit the Tottenham Hotspur Stadium on Thursday night, before West Brom’s trip to north London at the weekend.