Real Madrid president Florentino Perez is ready to back his manager, with the Spanish club growing increasingly confident of luring the Portuguese centre-back to the Bernabeu.
Manchester City are prepared to resist any approach and fight to keep hold of their defender.
Incoming City manager Enzo Maresca regards Dias as a crucial figure in his plans, with the departure of John Stones adding further weight to his importance at the back.
Manchester City signed Dias from Benfica in a deal worth around £60m in 2020.
He has gone on to win 11 major trophies during his time at the club, including the Treble in 2023.
The exit of Pep Guardiola has cast fresh doubt over the futures of several senior City players, Dias among them.
The defender remains under contract until 2028, but having achieved success at every level with City, a new challenge could appeal.
Dias is currently part of Portugal's World Cup squad and is focused on the tournament rather than his club future.
Mourinho is understood to see Dias forming a central defensive partnership with Antonio Rudiger if the move goes through.
Real are also keeping a close watch on his City team-mate Rodri as they continue to plan for the summer window.