Griezmann continues to be linked with a move to Old Trafford and this week fuelled speculation that he could join United by saying there is a "six out of 10" chance the move will happen.
Herrera is impressed with the 26-year-old's ability and appears ready to welcome him with open arms.
"Griezmann is a brilliant player, a phenomenon," Herrera told Cadena Ser.
"He is a star and all the teams in the world would want him.
"I have said it in the past, after Cristiano Ronaldo and Lionel Messi, he is in that group of players that can become their possible successors.
"However, Griezmann is still an Atletico Madrid player and I respect Atletico and their fans."