Following his release from Leicester, the 35-year-old signed a short-term deal with the Red Devils for their pre-season schedule.
Evans was only expected to remain with the squad for their friendlies against Lyon and Wrexham.
He came off the bench against the former and started against the latter as United won 1-0 and lost 3-1 respectively.
talkSPORT revealed earlier in the month that his deal with the club could be extended.
Boss Erik ten Hag has now hinted at such a prospect as he continues his preparations for the new season.
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The Dutchman said: "We need the numbers in the coming days in training.
"As you see, Fred is not here and also [Anthony] Elanga went back [to join Nottingham Forest].
"We need the numbers for proper training to hit our targets and that's the reason they are here."
Evans is one of United's successful academy products, with the centre-back making his senior debut in 2007.
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After 198 appearances in nine years, in which he won three Premier League titles and the Champions League, he left for West Brom.
The centre-back spent three seasons with the Baggies before completing a switch to Leicester in 2018.
Evans won the FA Cup with the Foxes three years later and featured 152 times across all competitions before his departure.
Since returning to United, he has bagged crucial minutes in friendlies as he builds up to the new season.