A report in British newspaper The Sun, which quoted an unnamed United source, claimed Pogba and Lukaku had a row over a penalty during Saturday’s game at Old Trafford.
Lukaku had already struck twice to help give United a 3-2 lead when Ole Gunnar Solskjaer's side were awarded a late spot-kick.
Pogba, who is United’s regular penalty taker, stepped up to take the kick, rather than allowing Lukaku the chance to seal a hat-trick, and the France midfielder saw his effort saved by Southampton goalkeeper Angus Gunn.
It has since been claimed that Lukaku confronted Pogba in the dressing room following the match and needed to be calmed down by Solskjaer.
Lukaku appeared to deny those claims in a cryptic message posted on Twitter , with the former Everton striker saying: "When the hate don't work they start telling lies.”
Now Pogba has followed Lukaku’s lead by appearing to play down reports of a rift on social media.
Posting to his Instagram account, Pogba wrote: "When the hate don't work they start telling lies... Hahahahaha people are too funny bro."
Pogba and Lukaku have long been considered close friends, with the pair even holidaying together when in 2017, just prior to the Belgian joining United from Everton.
Both players have been in fine form in recent weeks and have clearly benefitted from the appointment of Solskjaer as interim United manager in December.
Lukaku had scored just twice in 17 matches under Jose Mourinho before the Portuguese’s dismissal but has scored seven in 14 games under his successor Solskjaer.
Pogba has enjoyed a similar resurgence, scoring nine goals in 16 appearances under the Norwegian having scored just five goals all season prior to that.
Lukaku is expected to start for United in Wednesday's Champions League last-16 second leg against Paris Saint-Germain, but Pogba is suspended after being sent off against the Parisians at Old Trafford last month.
The Red Devils trail 2-0 from the first leg and will need to produce something remarkable in the French capital if they are to reach the last eight.