The Spain midfielder is out of contract next year and his camp are pushing for feedback before any ultimatums start being issued.
Herrera has made just 31 appearances this season and has been further squeezed out by the recent emergence of youngster Scott McTominay at Old Trafford.
United boss Mourinho, however, remains a fan of Herrera's attitude and there could still be a chance he is kept around longer, should the 28-year-old be ready to accept that he is considered no more than a squad player these days.
The Red Devils are planning to bring in at least one more midfielder this summer, with Shakhtar Donetsk's Brazilian star Fred seen as a realistic target.
Herrera knows there would be interest back in Spain but he is happy in Manchester and wants to continue plying his trade at the Theatre of Dreams.
Mourinho is thought to be planning a clear-out in the close season of several members of his squad and Herrera's £130,000-per-week wages could yet be a factor in the overall decision-making process.
United signed him from Atletico Bilbao for £27m back in 2015 and know they can recoup a sizeable portion of that figure if they do ultimately decide to sell the Spaniard.