Eight years after leaving Old Trafford for the first time, the 36-year-old made a comeback to United last summer from Leicester City.
The Northern Ireland international began working out with the team in the preseason in order to stay fit, but after making an impression on Erik ten Hag, he was given a one-year contract.
Evans continued to play in 30 games the previous season, making an appearance as a substitute in the FA Cup victory at Wembley over Manchester City.
The team has also stated that they are still in talks with goalie Tom Heaton about a new contract, and Omari Forson has received an offer of employment.
Forson, 19, made his Premier League debut against Wolves in February, winning 4-3.
when, at Molineux, he assisted Kobbie Mainoo in winning.
The forward, who was born in London, made six further appearances before leaving the team without agreeing to a new contract.
On June 30, when their contracts expire, Raphael Varane, Anthony Martial, and Brandon Williams will all be freed.
Williams played for Ipwich on loan during the previous season, but he returned to United on December 29 due to an injury.
