"I have not asked for any signings and I have been clear I wouldn't like it if anyone left," the Portuguese told reporters.
"The players know it, the board of directors too," said Mourinho ahead of Tuesday's King's Cup last-16 first leg tie at home to Malaga. "I would like to start and finish the season with the same players."
Some of the squad members at La Liga leaders Real that rarely get playing time have been linked in the media with moves to the English Premier League, including Spain centre back Raul Albiol and midfielder Esteban Granero.
Argentina striker Gonzalo Higuain, who competes for a place in the forward line with France international Karim Benzema, is a target for Chelsea, according to reports.
Turning to Tuesday's game, Mourinho said Malaga would want to prove their mettle after spending more than €100 million on players since they were bought by a member of the Qatari royal family in June 2010.
"We are speaking about a team that made a huge investment and for sure they want a return and I think the cup is a target for them," added Mourinho.
If Malaga can get past holders Real their opponents in the last eight will be 2011 runners-up Barcelona or Osasuna, who play their first leg at the Nou Camp on Wednesday.
Mourinho will be without Spain defender Sergio Ramos and Argentina winger Angel Di Maria for the game at the Bernabeu. Both players have minor muscle tears were left out of the squad, Real said on their website.
