Cech, who lost his place in the starting line-up to Thibaut Courtois this season, has been linked with Arsenal, Manchester United and Paris Saint-Germain.
Mourinho has made no secret of his desire to dissuade Cech from leaving Stamford Bridge, but accepts that the final decision on his future will be taken by Blues owner Roman Abramovich.
"You have to accept any decision that the owner will have in relation to Petr, but I am different," Mourinho told reporters at the launch of BT Sport's European football channel. "I have the same respect for Petr that everyone at the club has, but my answer [if he can join Arsenal] would be no way. If he answer is different, then I will accept.
"My answer is not important to this question because the owner is a person with the perspective that I admire a lot. He respects people who do important things for him and since 2004 to 2014-15, he has given great service to the club, unbelievable behaviour."
Should Cech decide to join one of Chelsea's Premier League rivals, Mourinho confirmed that he will try and secure a swap deal.
"For every club that is interested in Petr, I can find players in that team that I like too," he said.
When asked about who would be Chelsea's main threat next season, Mourinho was quick to choose Arsenal as he believes the Gunners have a brilliant squad and a fantastic manager. Arsene Wenger's side finished third this season after winning 22 of the 38 Premier League games they played.
"I think Arsenal have a fantastic squad, probably much better than people think," Mourinho said. "Normally you say if you win a lot of titles then you have a fantastic squad, but they have a fantastic squad anyway.
"I believe, and I am not making fun here, that they have a top manager. I think they have everything. They were an opponent this season, but next season they will be even better."