And Zidane has been at the forefront of the Spanish giants’ pursuit, openly discussing the midfielder.
Solskjaer has made a point of refusing to talk about transfer targets this summer and, privately, has been angered by his Real counterpart’s lack of discretion.
Zidane mischievously hinted in March that Pogba wanted to join him at Real, stating: “He’s always said that he likes Madrid.”
Those comments were not appreciated within Old Trafford, where it remains their determination to keep hold of the World Cup winner.
And while Pogba has also publicly stated his desire to leave United, the belief within the club is that Real do not have the funds to meet their £150m-plus asking price.
Which is why Solskjaer has taken such exception to Zidane’s comments, which are only likely to further unsettle the player.
United have already rejected Real’s offer of a player-plus cash deal involving James Rodriguez and £27.6m on top.
It was considered a derisory bid and evidence of Real’s lack of spending power following the signings of Eden Hazard, Luka Jovic, Eder Militao, Ferland Mendy and Rodrygo this summer.
But Zidane is desperate to land the France international – and the ongoing uncertainty over his future has seen United step up interest in Christian Eriksen.
Eriksen has long-been on a list of potential replacements for Pogba – even if a deal for the Tottenham playmaker is considered difficult to pull off before Thursday’s transfer deadline.
Solskjaer has already spent £140m on the signings of Harry Maguire, Aaron Wan-Bissaka and Daniel James.
He would like to bring in a midfielder and attacker before the deadline – but after United pulled the plug on a swap deal between Romelu Lukaku and Paulo Dybala, time is running out to bring in more recruits.
Talks over Juventus forward Mario Mandzukic have also stalled.
Solskjaer is said to be comfortable heading into the new campaign with no more additions, but the pursuits of Dybala and Mandzukic are evidence of his attempts to further strengthen a squad that finished sixth last season and missed out on the Champions League for the third time in six years.