Los Blancos are 'increasingly confident' a deal can be done with Manchester United for the wantaway midfielder, according to ESPN.
Madrid president Florentino Perez was understood to have told manager Zinedine Zidane that a move for Pogba would be difficult, in a Montreal meeting last week.
Madrid had already spent around €300 million on incomings this summer, and Pogba is thought to be valued by Manchester United at €180m.
However, the report claims that Zidane has emplored the Madrid hierarchy to push as hard as possible, and there is now a renewed belief that a deal can be done.
It's added that Zidane has insisted he has enough numbers in attack to account for Marco Asensio's long-term injury, and he would rather they focused on Pogba.
The largest stumbling block is the Premier League's fast-appraching transfer deadline on August 8.
This means Manchester United only have two weeks to replace Pogba, and they will not sell the Frenchman if they can't.
Another headache for Madrid is Gareth Bale's seeming immovability, as Zidane struggles to free up his squad and wage space this summer.
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