The Red Devils released a video on their official Twitter account of the players and staff on a walk around Perth ahead of their first friendly match in the city on Saturday.
A small section of the footage shows Pogba and Lingard in animated discussion before Swedish defender Victor Lindelof holds the French World Cup winner back from approaching his English team-mate.
While the context of the incident is unknown, Pogba's apparent disagreement with Lingard comes with his Old Trafford future in question after his agent Mino Raiola admitted the player was 'in the process' of a transfer away from the club.
Watch the incident between Pogba and Lingard in the video below.
Pogba, who has been consistently linked with a move to Real Madrid or Juventus all summer, recently stoked speculation by suggesting 'it could be a good time to have a new challenge somewhere else' .
The 26-year-old's participation in United's Down Under tour looked in doubt in recent days with video emerging of a training session at New York's Central Park while his team-mates had started pre-season training at the club's Carrington facility.
However, Pogba was named in the club's squad for the tour and was then pictured looking downcast , along with transfer-linked team-mate Romelu Lukaku, as he prepared to board Manchester United's private jet for the journey to Australia.
His recent behaviour has been questioned by a number of former United players, including compatriot Louis Saha, who said he was a 'bit annoyed' by Pogba's recent conduct .
Ole Gunnar Solskjaer's side will take on A-League club Perth Glory on Saturday before meeting old rivals Leeds United on July 17.