The 26-year-old is understood to have had back-to-back nights out Thompsons Garage nightclub.
He was seen leaving the nightclub on Thursday evening, before flying back by private jet the following morning - as first reported by The Athletic.
Erik ten Hag said that Rashford had been unable to train on Friday, ahead of their FA Cup clash with Newport on Sunday, due to illness.
The Red Devils boss said: "This morning, Rashford was ill and (Jonny) Evans was ill so we have to see how they recover."
Manchester United did not comment when approached.
The United players had been given time off ahead of their FA Cup clash on Sunday, following their 2-2 draw against Tottenham on January 14.
They returned this week and Rashford is believed to have been involved in sessions between Monday and Wednesday.
It is believed the forward was there to see former academy teammate Ro-Shaun Williams - who recently signed for Northern Irish side Larne.
It is not the first time Rashford's attendance at a nightclub has got him in hot water.
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He was pictured going out after their 3-0 derby defeat to Man City in November.
"I spoke with him about it. It's unacceptable. He apologised and that is it. For us it's an internal matter," Ten Hag said.
"He's 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."