The 27-year-old emerged as a major doubt for the contest at Goodison Park when he picked up a pelvic issue while representing Cameroon against Mauritius on Friday.
The injury led to Onana withdrawing from his national team's squad ahead of the clash with Libya, and there had been fears that the stopper could be facing a period on the sidelines.
However, according to Italian journalist Fabrizio Romano, medical examinations showed that the summer arrival from Inter Milan had only suffered a «small injury».
Romano claims that Onana has been working with the main group at the Carrington training complex, so he is set to be available for selection against Everton, with Altay Bayindir being made to wait to make his debut for the 20-time English champions.
There has been criticism of Onana's form since arriving at Old Trafford, with the Cameroonian conceding 30 times in his opening 18 appearances for Man United.
However, the goalkeeper has managed to produce back-to-back shut-outs in the Premier League against Fulham and Luton Town, and he has made important saves in both of those contests.
Man United have had Luke Shaw back in full training this week for the first time since suffering a hamstring injury more than three months ago.
Lisandro Martinez also watched his teammates train at Carrington on Wednesday, but the Argentina international, who is recovering from a second foot operation of the year, will not be available for selection this side of Christmas.
Man United will also definitely be without Casemiro, Jonny Evans, Christian Eriksen, Tyrell Malacia and Amad Diallo for the clash with Everton
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