The 19-year-old Brazil under-20 international was thought to be on the verge of joining Sir Alex Ferguson's side last summer.
However, the Samba starlet's former employers Gremio denied him the opportunity to take part in a trial with the Old Trafford outfit, and instead sold him to last year's UEFA Cup winners Shakhtar who possess seven other imports from Brazil.
Costa - who joined the Ukrainians on a five-year-deal - recently featured against Fulham in the Europa League, with Roy Hodgson's men triumphing 3-2 on aggregate before later eliminating Juventus and German champions Wolfsburg.
But, according to the News of the World, the youngster recently announced at a press conference that he still hopes to complete a move to Manchester later in his career.
"If I had the choice, I would still like to play for United," he said.
"I know definitely that United sent a fax to my club Gremio asking to release me to their training ground for a trial. But the board of Gremio refused their request and said I already had the ability to play at the top level. They wanted United to sign me without trials.
"They were not ready while Shakhtar signed the contract with me on the terms of Gremio."
