Club captain Valencia and Herrera are two of 14 players released this summer. Herrera is expected to join Paris Saint-Germain on a free transfer.
Mata is out of contract on June 30 but has not been officially released because he has an offer on the table. Sources have told ESPN FC that the Spain international is still in talks with the club.
As well as Herrera and Valencia, James Wilson, who scored twice on his senior debut as a teenager in 2014, will also leave Old Trafford this summer.
Millen Baars, Joshua Bohui, Zachary Dearnley, Callum Gribbin, DJ Buffonge, Regan Poole, Tom Sang, Tyrell Warren, Callum Whelan and Matty Willock have also been released along with United States international Matthew Olosunde.
Sources have told ESPN FC that Olosunde, who made his senior international debut last year, is hoping to extend his stay in Europe, preferably with another English club, rather than return to MLS.