The 26-year-old participated in training on Wednesday and was photographed at Lavery's Bar that evening before a scheduled day off.
It is understood that he visited Northern Ireland to spend time with his friend and former academy teammate Ro-Shaun Williams, who is currently signed with Larne FC.
The United star was later spotted at Thompson Garage nightclub on Thursday and reportedly flew home via a private jet the following morning.
According to The Sun, Rashford reported feeling unwell ahead of Friday's training before Manchester United's FA Cup fourth-round trip to Newport County on Sunday, which Ten Hag confirmed in his pre-match press conference.
"This morning, Rashford was ill, and Evans was ill. So we have to see how they recover, but we have, for the rest, players returning, like Martinez, like Shaw, like Maguire, like Casemiro, which is a good thing," the United boss said.
Shortly after Ten Hag's comments, videos surfaced on social media showing Rashford partying in Belfast hours before Friday's training session.
The report adds that the England international could find himself at risk of punishment after he was slammed by the manager for going out clubbing after United's defeat to Manchester City back in October.
Ten Hag addressed the matter on that occasion, stating: "I spoke with him about it. It's unacceptable. He apologized, and that is it. For us, it's an internal matter."
The Dutchman added: "He [Rashford] is very motivated to put things right. He's totally with us. He has made a mistake but that doesn't say he's not fitting in.
I see him every day in training, what he's doing, I know."
Back in December 2022, the United boss made the decision to drop Rashford from the starting lineup against Wolverhampton Wanderers after the player overslept and was late for a meeting.
Despite netting in two of his last three matches, the 26-year-old has endured a frustrating season, scoring just four goals across all competitions, compared to the 30-goal tally he managed in the last campaign.
The Red Devils will face Newport on Sunday, and after finishing at the bottom of their Champions League group and being eliminated from the Carabao Cup, the FA Cup is likely the only chance for United to claim a piece of silverware this season.