The United star has been playing with a swagger ever since Mourinho was sacked back in December.
But Tuttosport says that, despite Mourinho's exit, the United star is still eager to leave Old Trafford behind.
It is claimed he made a phone call to Juventus in January admitting that he is eager to return.
However, Juventus ultimately opted against pursuing their former midfielder.
But the Serie A giants could use Douglas Costa as a bargaining tool in any potential negotiations.