Mourinho brought Essien to Stamford Bridge in August 2005 for a then-record £24.4million fee from Lyon.
The Portuguese boss borrowed the 30-year-old for the 2012/13 campaign at the Bernabeu and has used him in a variety of roles, including both full-back positions.
The Ghana international midfielder has started 18 games in total in La Liga and a further six in the Champions League.
In June 2010, Essien extended his Chelsea contract until summer 2015 and with his knee injury problems seemingly now behind him, he hopes to continue his career at the Bridge - especially if Mourinho comes back for a second stint in charge.
"We have a very good relationship," said Essien, quoted in The Sun.
"I understand him very well.
"Daddy knows I can play in any position he wants me to, except goalkeeper."