Mourinho brought Costa to Stamford Bridge in 2014 and was integral to them winning the Premier League that season.
But the Spanish striker came in for criticism when Mourinho was sacked in December 2015 after nine defeats in 16 matches.
Chelsea stars in training as full-strength Blues prepare for Man United clash Fri, April 14, 2017
Express Sport brings you the best pictures from Chelsea's latest training session as the Blues prepare to take on Manchester United at Old Trafford on Sunday (4pm)
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Chelsea were hard at work in training ahead of their clash with Man United
And Costa insists he is grateful to his former boss.
Diego Costa is still respects Jose Mourinho
He told Sky Sports: "In all honesty I always tell people that I am grateful to Mourinho because he helped me a lot.
"As a player when you want to improve you always look for the best coach and Mourinho is one of the best.
Jose Mourinho will face off against Diego Costa on Sunday
"I wanted to come to Chelsea because of Mourinho. When I considered Chelsea I thought about the fact that Mourinho was here.
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"He is a coach that demands a lot from his players, he wants the maximum.
"He helped me a lot and then what happened is that the following season didn't go well, these things that happen, but the truth is that Mourinho helped me a lot to improve as a player."