De Gea has long been linked with a move to Real Madrid, and came close to joining the Spanish giants in the summer of 2015 before the deal fell through at the final moment.
Herrera has spoken of the importance of the United fans in keeping the 27-year-old in England, and has tipped the stopper to again show his class next season.
"I remember that difficult summer when everyone was talking about Real Madrid and he played the first game at Old Trafford and everyone was singing his name and he told me 'this is amazing, they are the best'," Herrera told reporters.
"He can be very calm but he's the best. He will show it again. He's the best keeper I've ever seen in my life and he is with us so we have more chances to win titles."
United will continue their pre-season preparations with a clash against San Jose Earthquakes on Sunday night.