The Frenchman admitted publicly during the FIFA international break that a move to Madrid would be “a dream” for anyone.
His comments however threw his future at Old Trafford into doubts, with a section of United fans demanding the 2018 World Cup winner be sold on social media.
Solskjaer has held private talks with the star midfielder to interrogate his future at the Manchester outfit.
According to reports filtering through in the UK, the Norwegian tactician pulled Pogba aside during a training session and asked the midfielder to see him in his office.
The 46-year-old went on to make it clear to the former Juventus midfielder to forget a possible summer move to Real Madrid.
Pogba has over two years to run on his current deal at United, with the club having an option of extending that by a further year.
A Champions League qualification could however prove critical to keeping the Frenchman at Old Trafford.