(CNN) -- Inter Milan president Massimo Moratti has admitted he is resigned to manager Jose Mourinho leaving the club to join Real Madrid.
Moratti invited Mourinho to dinner at his house on Monday night and tried to convince the Portuguese coach to stay in Italy.
Mourinho steered Inter to the treble of Italian league, cup and European Champions League this season, but has been strongly linked with a move to the Spanish capital.
"There's always hope, but we also have to respect the wishes of someone who thinks he has fulfilled his duty," Moratti told Inter's Web site.
"The approach of the coach is that of someone who is already thinking of going to Real Madrid," he added in quotes carried by the UK Press Association.
Mourinho, who previously coached Porto and English champions Chelsea, declined to comment on his future following the meeting with Moratti.
"The only thing that I can say is that I have enjoyed very much eating with my president. You always eat well at Moratti's house," he told PA.
Meanwhile, former Inter player and coach Sinisa Mihajlovic has quit as coach of Catania, fueling speculation he could be in line to replace Mourinho at the San Siro.
"I hope to soon find a job which legitimizes my decision and my professional ambitions," the Serbian told Inter's Web site.
Elsewhere, Jean Tigana has been named as the new coach of French Ligue 1 side Bordeaux.
Former France midfielder Tigana, who has previously coached Fulham in the English Premier League, replaces Laurent Blanc, who is taking over as France coach after the World Cup in South Africa.