The Bayern Munich defender's time at the club appears to be over, especially after he was left out of the side in their 4-0 win over Werder Bremen on Friday.
Pavard started in the German Super Cup against RB Leipzig, but was taken off at half-time with the Bavarians 2-0 down.
Manager Thomas Tuchel then opted to start with Moroccan Noussair Mazraoui instead for their Bundesliga opener over the weekend.
Gazzetta dello Sport claims that Inter have increased their offer and are confident of getting the deal over the line.
However, despite the agreement, Bayern are stalling the deal until they find a replacement for Pavard.
Mazraoui would be the only current fit right-back at the club if Pavard was to leave, after the club allowed Josip Stanisic to move to Bayer Leverkusen on loan this week.
Inter will hope the French World Cup winner can provide competition to Matteo Darmian, who, like Pavard, is a converted right centre-back after starting off as a right-back.
Simone Inzaghi's preferred tactic of playing three-at-the-back will likely see the French international used on the right of the three.
Inter already have two options at right wing-back, following the arrival of Juan Cuadrado in the summer to fight for a starting spot with Denzel Dumfries.
Pavard often played as a right-back in a back four with France and Bayern, but he does have experience in a back three too.
A move for Pavard makes sense given that Inzaghi does not have an exact like-for-like replacement for Darmian in the squad.
New signing Yann Aurel Bisseck had played in the wide spots of a back three with former club Aarhus, but he was mainly deployed on the left.
Man United are said to still be in the hunt for a defender this summer, and their 2-0 defeat at Tottenham Hotspur over the weekend may intensify that search.
After Harry Maguire's move to West Ham United fell through though, United will need to recoup funds from some other players in the squad in order to buy.
Maguire was unused once again at the weekend, but the England centre-back looks set to stay and fight for a place under Erik ten Hag.