Perisic is out of contract at Italian giants Inter this summer and has yet to decide on his next move, despite the Nerazzurri looking to keep hold of him on a fresh deal.
He has interest from several clubs and Tottenham have intensified their efforts to land him in recent days.
Now they are closing in on Perisic and it has been claimed they are the favourites to snap him up on a two-year deal worth over £4m per year.
Chelsea and Juventus are suggested to be ready to strengthen their proposals for Perisic, who will make a final decision on Monday, but Tottenham appear to be in the driving seat.
Conte held talks with Paratici on Friday and agreed to stay at Spurs, with signings key to his decision.
It is claimed that Perisic was discussed between the two men.
Tottenham finished fourth this season to qualify for next season’s Champions League and Conte wants Perisic, 33, to strengthen his options heading into a campaign where he will be looking to close the gap on the teams above Spurs.