Mourinho brought Costa to Chelsea from Atletico Madrid in 2014 and the Spain international repaid that faith by firing the Blues to the Premier League crown in his first season in England's top flight.
But a dreadful title defence followed, with Mourinho sacked as Chelsea lurched towards the relegation zone in December 2015 and Costa was one of a number of senior players to badly underperform amid rumours of dressing room unrest.
Costa was back on song at the start of this term under Antonio Conte, helping to establish a dominant position at the top of the league that they appear unlikely to relinquish.
Chelsea's two wins over United in the league and FA Cup this season have been testy affairs, with Mourinho respectively rowing with Conte on the touchline and drawing the ire of the Stamford Bridge faithful.
But Costa maintains significant respect for his former boss, who he credits as being the reason for him coming to England.
"In all honesty I always tell people I am grateful to Mourinho because he helped me a lot," he told Sky Sports ahead of Sunday's meeting at Old Trafford.
"As a player when you want to improve you always look for the best coach and Mourinho is one of the best.
"I wanted to come to Chelsea because of Mourinho. When I considered Chelsea I thought about the fact that Mourinho was here.
"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 happen, but the truth is that Mourinho helped me a lot to improve as a player."
Costa has 17 goals in the Premier League this season, although only three of those have come since the turn of the year after speculation linked him with a move to the Chinese Super League.