Woodward personally told Mourinho about his dismissal during a brief meeting at the clubs training ground on Tuesday morning.
Mourinho and Woodward had been at odds over the clubs transfer transfer policy since the start of the summer, with Mourinho demanding that a new central defender was signed.
Woodward, however, refused to meet Mourinhos request and opted against making what would have been the third centre-back signing of the Portugueses reign after Eric Bailly and Victor Lindelof.
According to The Sun, Mourinho discovered that Woodward has in fact been working on a deal to sign Costa from Juventus.
The Brazil international is struggling for playing time at Juventus after the Serie A champions permanently signed him from Bayern Munich for £36 million in the summer.
And Woodward wants to bolster Uniteds attack with Costas arrival in January.
The report also claims that before he was sacked, Mourinho was told that United will also be looking to sign a new central defender in January.
Ole Gunnar Solskjaer is taking charge of United on an interim basis until the end of the season with Mike Phelan returning to the club as his assistant.
Tottenham boss Mauricio Pochettino is Woodwards long-term target to replace Mourinho but Spurs will demand a hefty fee for the Argentina after he signed a five-year contract extension in May.
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