Chelsea and Arsenal have told Real Madrid there is no chance of their managers leaving in the summer.
Mourinho and Wenger were on a shortlist of seven
Real president Fernando Martin named Jose Mourinho and Arsene Wenger on a managerial shortlist on Monday.
"Arsene Wenger has repeatedly made his position clear. He is happy here and is not planning to move," an Arsenal spokesperson told the Evening Standard.
A Chelsea representative said: "Chelsea and Mourinho are united in an exciting and long-term project."
Real are looking for someone to succeed Juan Lopez Caro, who was promoted from the B team four months ago to replace Wanderley Luxemburgo.
REAL MADRID'S SHORTLIST
Arsene Wenger (Arsenal)
Jose Mourinho (Chelsea)
Rafael Benitez (Liverpool)
Sven-Goran Eriksson (England)
Marcello Lippi (Italy)
Carlo Ancelotti (AC Milan)
Fabio Capello (Juventus)
England boss Sven-Goran Eriksson and Liverpool's Rafael Benitez were also named on Real's shortlist.
The other prospective managers were all Italian - AC Milan's Carlo Ancelotti, Juventus' Fabio Capello and Marcello Lippi, coach of Italy's national team.
Martin said: "We are clear about the type of coach we want.
"We want one of the coaches you all know we want - Mourinho, Capello, Benitez, Wenger, Ancelotti, Lippi or Eriksson."
Wenger, Benitez and Capello have all distanced themselves from the job in recent weeks.