The Northern Ireland international signed a short-term deal with the Red Devils earlier this month after making a strong impression while training with the club at their Carrington training complex following his release from Leicester City.
Evans was involved in the pre-season friendly with Lyon in Edinburgh on July 19, and he has now travelled to the United States for Tuesday night's contest with Wrexham.
The 35-year-old will feature alongside a number of Man United youngsters in San Diego, with the first team having a friendly against Real Madrid on Wednesday night.
As it stands, Evans's deal will expire after the game with Wrexham, but there have been suggestions that he could potentially be handed a long-term deal.
Ten Hag was asked about the situation during his press conference on Monday and refused to reveal any details when it comes to the club's plans for the centre-back.
"I think he helped us, as you said, younger players, but also for the numbers here. Not all of the internationals were in and then we have to manage the load from the players," Ten Hag told reporters.
"So that was really useful. And Jonny wants to stay fit. He wants to still have a career. Last week, I think he played a very good game against Lyon and you could see how he was mentoring the younger players and I think he was pushing the younger players to a higher level and that can be really helpful.
"So I'm happy, we bring him now in. He will be tomorrow (Tuesday) in that game. So I'm happy he wants to do that and I think we help him as well."
Evans, who left Leicester when his contract expired on June 30, previously represented Man United between 2006 and 2015, featuring on 198 occasions for the club.
Ten Hag also provided a positive update on Amad Diallo's fitness on Monday, with the Ivory Coast international making a quick recovery from the ankle issue that he suffered against Arsenal on Saturday.
"It's not too bad. And today he was running again, not involved in the group, but we hope he can join tomorrow (Tuesday) in the training," the Dutchman said.
Sonny Aljofree, Toby Collyer, Will Fish, Isak Hansen-Aaroen, Elyh Harrison, Joe Hugill, Marc Jurado, Willy Kambwala, Charlie McNeill, Dermot Mee, Mateo Mejia, Maxi Oyedele, Logan Pye and Shola Shoretire have all travelled to the United States alongside Evans with a view to being involved against Wrexham.