The 18-year-old has been a key part of United's youth and reserve teams since arriving from Anderlecht in 2011, and has joined the senior squad on the club's pre-season tour of Asia and Australia this summer.
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"It will maybe be a chance for me to play there, so we will see in the future what will happen," he told reporters. "I think it's a big season for me. I've tried to impress the manager and try to play regularly.
"I worked hard last season. I didn't play in my favourite position, more as a striker, but I think I did well.
"I've tried to do my best and worked hard on the pitch but it's hard for us as well, with all the travelling and moving between different countries and time zones. I've tried to impress the manager and make sure I give myself the chance to stay with the first team."
Januzaj's contract expires in two years' time, and is hopeful he can secure a long-term deal with the club.
"I don't decide what happens with my contract," he added. "I've got people behind me who do this for me. Manchester United are a big club, I love it here, I feel good, so I hope to stay.
"My dad does everything for me. He just told me to work hard on the pitch, which is what I try to do."