Former Barcelona and Roma boss Enrique has been installed as the bookies' favourite to succeed the Italian should he move on in the coming months, although Chelsea could face competition from domestic rivals Arsenal.
Conte knows Enrique well from their time in Serie A and is full of praise for the currently out-of-work manager.
"I have spoken with him, and he's a really good person," Sky Sports News quotes him as saying. "I have great admiration for Luis Enrique and he is a fantastic coach.
"He reached his targets with Barcelona, and also with Roma. You could see a well-organised team. I can speak about him very well, as a person and a coach.
"We do this job, and our job is not 'difficult', but you must be open and understand the situation can change. A club can take different decisions. It's the same for me.
"But, I repeat, I'm not jealous or envious of other managers. Everyone knows his job, his work. I have, usually, a great respect [for fellow managers]."
Enrique quit Barcelona at the end of last season, leaving with eight major honours under his belt from his three years in charge.