The £25m former PSV Eindhoven forward, 22, started against Norwich and came off the bench against Bournemouth, but has been left out of Louis van Gaal's squad that travelled to London.
According to one report, Depay has fallen out with Van Gaal and opted not to travel to Wembley.
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19-year-old defender Cameron Borthwick-Jackson turned out against Bournemouth, but joins Depay in being excluded from United's 18-man squad.
Depay was dropped from the United squad for their 0-0 draw at Crystal Palace in October, but last scored in the Europa League round of 32 against Midtjylland in February while his most recent goal in the Premier League came against Watford at Vicarage Road in November.
“It’s a bit of a shame really, because when he came, he came with a big reputation," said former United striker Dwight Yorke on talkSPORT.
"Coming out of Dutch football he’d done really well and scored a lot of goals, and he got off to the perfect start at Manchester United.
"We all thought: ‘Yeah, we’ve got someone here who’s a bit special who’s going to excite the fans.’
“Unfortunately it hasn’t worked out that way for him, and he’s found it very difficult.
“He’s been in and out of the team, and as the season’s progressed he seems to have struggled going forwards.”
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