The midfielder has emerged as a target for the Chelsea boss as he seeks to reinforce his squad in January, though Shakhtar Donetsk are holding out for a fee in excess of €28 million for the 24-year-old.
Nevertheless, Costa reiterated his desire to join the Premier League leaders, confessing his desire to work with Mourinho at Stamford Bridge.
"To play at Chelsea is a dream for any player," he told Globo Esporte. "It is standing next to some of the best players in the world and competing with the world's best as well.
"But really, what catches my eye is the coach. He is a very intelligent coach and has been victorious wherever he went. One of the things that would make me happier to act at Chelsea would be this."
Costa has spent five years working with Shakhtar manager Mircea Lucescu, having joined the club from Gremio as a teenager and, while he has praised the Romanian, he believes Mourinho would help him further evolve as a player.
"I learned a lot here with Lucesc," he added. "I arrived at Shakhtar aged 19 and he taught me a lot. I am very grateful. But I also know that with Mourinho at Chelsea, my progress would be even greater.
"He has won just about everything. He is among the best, if not the best. He is at the top."
