• Hughes: We want Kakuta
The former Chelsea boss wants to be reunited with Drogba, 32, after initial negotiations to recruit Manchester City's Emmanuel Adebayor broke down, the Sunday Mirror reports.
Mourinho is so eager to recruit a striker following a long-term injury to Gonzalo Higuian that he has fallen out with Real's general manager Jorge Valdano, who is reluctant to recruit another forward on a permanent basis with out-of-favour Karim Benzema sat on the Bernabeu bench.
Valdano was asked after last Sunday's draw with Almeria about the progress being made in the hunt for a new striker and he said: "We are spectators to whatever the coach decides. I hope Benzema does not stay on the bench for too long. The situation surrounding him is unfair."
Mourinho responded: "I pick the team, and if I need any help then I have my coaching staff."
Despite the tensions at Real, the Spanish club were in talks to take Adebayor on loan but when City demanded a £15 million transfer the move broke down.
Drogba, who joined Chelsea at the same time as Mourinho in 2004 in a £24 million deal, has been out of form since contracting Malaria last year, but Real will send a team of scouts to London to evaluate the striker.
The Sunday Times reports that the Drogba, 32, is top of a list of senior players set to be sold as Chelsea plan a major overhaul of the squad which won three titles in six seasons but is now showing its age.
However, Blues boss Carlo Ancelotti is adamant his current first-choice XI is not over the hill. He said: "Do you know what is the oldest team in the world? Inter Milan - 29.6 years average.
"Another question: who was the winner of the Champions League last year? We are not the oldest because the oldest is Inter.''
Nevertheless, with key men like John Terry, Frank Lampard and Drogba the wrong side of 30, there will come a time in the not-too-distant future when Chelsea will need to consider life without them.
Ancelotti believes there are ready-made replacements at Stamford Bridge in the shape of Branislav Ivanovic, Ramires, Josh McEachran and Daniel Sturridge.
"If you mention Terry, Lampard and Drogba, I would like to continue to have this kind of player,'' Ancelotti said."We can mention Ivanovic, we can mention Ramires, we can mention Sturridge, we can mention McEachran. They are our young players, they are improving and growing in this club.''