Pogba has long been linked with a move to Madrid, but when the English transfer window closed last week it seemed unlikley that a deal would be done.
Manchester United didn't sign a central midfielder in the end, which suggested that Pogba would be staying put.
However, Mathias Pogba told El Chiringuito (via Marca) that his brother is still angling for a move away from Old Trafford.
"Paul wants to go. He can't do everything at United," he said on Spanish TV.
"The player that Zidane is missing is Paul. It's not impossible for Florentino to sign him.
" Ican't guarantee that Paul will continue at United. Until September 2, anything can happen. Madrid needs the football and joy that Paul brings."
Pogba played a key part in United's 4-0 dismantling of Chelsea on the opening weekend of the Premier League season.
After the game, he highlighted the uncertainty surrounding his future, but also reassured fans that he remains commited.
"Obviously there have been things said, but only time will tell. This question mark remains," said the Frenchman.
"However, I am here in Manchester. I enjoy playing with my team-mates and I always want to win every game. I always give it everything.
"I am always good whenever I play football. It is what I love — it's my job. I give the maximum each time."
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