French World Cup winner Pogba was heavily linked with a move to Madrid last summer but United chief Ed Woodward blocked the move.
But, one year on, Pogba is still determined to force through a move to the Bernabeu and has told close pals he does not see his future in Manchester, according to the Daily Mail.
Real Madrid and returning manager Zinedine Zidane are equally keen to see Pogba arrive through the doors as they look to compete domestically and in Europe next season.
Manchester United have insisted that Pogba, who returned to Old Trafford in 2016, is not for sale and Woodward is believed to be personally desperate to keep hold of the midfielder.
But it is claimed United will listen to offers in excess of £160million, knowing there is little point in keeping Pogba at the club against his will.
Pogba, according to the Daily Mail, is concerned by Manchester United’s lack of progress since his high-profile return three years ago.
While his mood improved after Ole Gunnar Solskjaer replaced Jose Mourinho, the 26-year-old is said to see his long-term future in Madrid.
Pogba’s chances of leaving will strengthen if the Red Devils, as expected, fail to qualify for the Champions League. Solskjaer’s side are currently sixth with two matches remaining.
Solskjaer, who has seen his team struggle over the past six weeks after an initial lift following his arrival, wants to sign two midfielders this summer, whether or not Pogba leaves.
Ander Herrera is expected to move on, while Juan Mata is also being strongly linked with a departure.
Speaking about Mata’s future on Friday, Solskjaer said: ‘It’s up to him. I’ve had words with him and he knows how highly I regard him.
‘I was so pleased for him last week; it would have been so much nicer for him to sit there and talk about Juan scoring the winning goal against Chelsea.
‘He’s a top pro and let’s see if they manage to agree.’
Pogba has been one of Manchester United’s best players across the 2018-19 campaign, scoring 17 goals and making ten assists in 56 games in all competitions.
Solskjaer’s side face Huddersfield Town on Saturday, before finishing the season at home to Cardiff City.