Spain international De Gea has continually been linked with a move to European champions Madrid after a transfer to the Santiago Bernabeu fell through in 2015.
Madrid's goalkeeping situation has dominated headlines again this off-season, with Chelsea's Thibaut Courtois also a candidate to swap London for the Spanish capital.
Red Devils team-mate Herrera, however, feels the loyalty of Manchester United's fans will keep De Gea at Old Trafford.
"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'," said Herrera.
"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."
De Gea was heavily criticised after Spain were sensationally eliminated by hosts Russia in the last 16 of the World Cup.
But Herrera backed his countryman to silence his critics with United in the Premier League this season.
"He is so, so strong," Herrera added. "I remember when I was in Spain and he signed for the club. The first couple of months were hard for him and he became the best goalkeeper in the world in the next four years so I am very relaxed about him.
"We are very lucky to have him because he is the best in the world. I don't care what the critics say.
"He is the best goalkeeper in the world, by far, and he will show it again. When you are the best goalkeeper in the world and you don't make those amazing saves, everyone is going to talk.
"When I don't play very well, I don't get that criticism because I am not one of the best in the world, but he is, so it's normal and he will cope with it."