De Gea, 24, has been repeatedly linked with Real Madrid with a little over a year remaining on his existing deal, which was signed when he joined United from Atletico Madrid in an ??18million deal in 2011.
Speculation over his future increased after United signed former Barcelona goalkeeper Victor Valdes on a free transfer, with manager Louis van Gaal saying he wants De Gea to stay but remaining non-committal over the progress of talks.
However, Mendes, appearing on Spanish radio station Cadena Ser on Sunday evening, said suggestions of a deal with Madrid are wrong and that talks had begun with United.
“It’s not true that the deal is done,” Mendes was quoted as saying by AS. “I am negotiating his contract renewal but we haven’t signed anything yet. As of this moment, we will see what happens.
“We’re holding talks and at this moment, it seems he could continue with United, but as I say, we haven’t signed anything yet.”