The Northern Irishman, who played for the Red Devils from 2006 to 2015, had been given a short-term summer deal to cover United's pre-season.
That now looks set to be extended which could push former captain Maguire even further down Erik ten Hag's centre-back pecking order.
Evans had previously signed on an U21 deal to maintain his fitness levels after leaving Leicester City, but now looks likely to stick around, according to the Daily Telegraph.
Evans has 198 United appearances to his name during his first stint at the club, winning three Premier League titles and two league cups.
Maguire has long held the title as the world's most expensive defender following his 2019 record arrival from Leicester, but is out of favour under Ten Hag.
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A total of 17 United squad members registered more minutes than Maguire last season, who even lost out to left back Luke Shaw at centre back late on in the season.
Following just 31 out of a possible 62 appearances during the 2022/23 campaign, Maguire lost the captain's armband to Bruno Fernandes, and now could find himself below Evans.
The news comes after Maguire failed to complete a move to fellow Premier League side West Ham, who were understood to have had a £30m bid accepted by United.
However, the Hammers grew tired of waiting for the deal to be completed and have since signed Konstantinos Mavropanos from Stuttgart for £18m.