The Spanish giants are keen to sign the French midfielder this summer while Pogba is desperate to work with Zinedine Zidane.
United's valuation of Pogba is £150million, but they will do well to receive as much as that now that it is clear their record signing wants out.
Both players have been linked with moves to Old Trafford in recent years and could now be used as makeweights.
On Sunday, Pogba said: "Like you said, there is a lot of talking and a lot of thinking as well.
"For me I have been for three years in Manchester and have been doing great, some good moments and some bad moments, like everybody. Like everywhere else.
"After this season and everything that happened this season, with my season being my best season as well... I think for me it could be a good time to have a new challenge somewhere else.
"I am thinking of this - to have a new challenge somewhere else."