Cech wants to leave Stamford Bridge after playing second fiddle to Thiabut Courtois this season, with Arsenal, Manchester United and Paris Saint-Germain among the clubs reported to be interested in signing the 33-year-old.
Abramovich is willing to grant Cech his wish of a move, but Mourinho admits he would not allow it were it up to him.
“The owner is the owner, he is the person with the perspective I admire a lot, respect a lot,” Mourinho said.
“He respects a lot of people who do important things for him. Since 2004 to 2014-15, 10 years of success with the club, 10 years of unbelievable behaviour.
“I will have to accept any decision that the owner has. I’m different. I have the same respect for Petr that everybody at the club has, but my answer would be no way. If the answer is different I will accept that.”
Asked if he thought Abramovich would ultimately let the player go, Mourinho said: “Perhaps. But if every club that is interested in Petr, I can find a player that I like in that team too.”