The pair are both out of contract at the end of this season and have still to agree new deals.
Mata and Herrera can leave Old Trafford as free agents on June 30 to join other clubs.
But negotiations with Manchester United bosses have stalled after it emerged both of them are demanding significant wage hikes.
United executive vice chairman Ed Woodward is refusing to bow to their demands and will not be held to ransom.
United are unwilling to meet the demands for Herrera and Mata, 29 and 30 respectively, which has led to a stalemate in talks with their camps.
Old Trafford sources have indicated Herrera’s representatives are asking for a contract extension towards the higher end of United’s pay scale.
Both him and Mata have seen Alexis Sanchez given a £500,000-a-week deal at Old Trafford and want a slice of the pie themselves.
But Woodward has told the midfielders to lower their wage demands if new deals are to be struck.
“Manchester United executive vice chairman Ed Woodward is refusing to bow to their demands and will not be held to ransom”
Reports claim both of them want deals in the region of £200,000-a-week.
Caretaker boss Ole Gunnar Solskjaer is keen for both of them to stay.
But Herrera is not a regular starter, while Mata is approaching the twilight of his career and Woodward wants to give them deals that reflect this.
United, meanwhile, remain in talks with David De Gea’s agent over a contract extension for the Spanish superstar.
His deal runs out at the end of next season, with United willing to hand him a deal worth £350,000-a-week.
This would make him easily the highest paid goalkeeper in world football.
But De Gea is holding out for closer to £500,000-a-week, which is proving a stumbling block for both parties.
De Gea has been a long term target of Real Madrid and wants United bosses to give him a deal that reflects his loyalty and level of performance.