Mata, who joined from Chelsea in January 2014, has been linked with a free transfer abroad.
But the former Valencia and Chelsea midfielder has been handed the chance to sign fresh terms by United, meaning he could yet extend his time at Old Trafford.
James Wilson and Regan Poole, who have both previously played first-team football, are among those to be departing United after spending the 2018-19 campaign out on loan.
And United have officially said goodbye to Herrera and club captain Valencia following the expiration of their contracts.
Also leaving are DJ Buffonge, Tyrell Warren, Matty Willock, Callum Whelan, James Thompson, Thomas Sang, Zak Dearnley, Matthew Olosunde, Callum Gribbin, Millen Baars and Joshua Bohui.
As well as offering Mata the chance to stay, Alex Fojticek, Paul Woolston and Luca Ercolani have also been offered new contracts. The Premier League side have also taken up the option to extend Aidan Barlow's deal.
United announced on Friday that a deal has been agreed with Swansea City for Welsh winger Daniel James as Ole Gunnar Solskjaer begins to reshape his squad.
Solskjaer is hoping to rebuild his team with a young English core following their dispiriting end to last season, when they tumbled out of the race for the top four following a succession of defeats.
Their loss to Barcelona in the Champions League quarter-final was a particularly eye-opening night for the Norwegian, highlighting the depth of the re-building necessary at Old Trafford after the hosts ran rings around his beleagured team.
Solskjaer's revival of the team left behind by Jose Mourinho started brightly, and he led the club back into contention for the top four from the depths of mid-table.
But their form collapsed in the spring, coinciding with the club's announcement that the caretaker boss had been given the job full-time.