The 19-year-old, who is a United States Under-20 international, joined Man United from the New York Red Bulls Academy in January 2016 after catching the eye of the Premier League outfit.
The full-back turned out for Man United Reserves during the 2016-17 campaign, but he also travelled with the first team for the Premier League games against Arsenal and Tottenham Hotspur.
"I'm very happy with how the season has gone," Olosunde told Man United's official website. "Just travelling with the first team was a big thing for me. It's a lot different when you are actually with them. You just think 'wow'!
"They're all friendly and talk to you to try to help you out. I was training with them for a bit and it was a great experience. I really enjoyed it. I would have loved to be involved in the matchday squad but it's good knowing, eventually, I could get my chance and I will just need to take it."
Olosunde has been tipped to travel with the Man United squad for their pre-season tour of the United States next month.