The 22-year-old is highly rated by Europe's top clubs after breaking onto the scene in the Bundesliga last season. The German scored 21 goals in 30 games during his debut season for the Red Bull-owned club.
Werner listed the Reds and United as his favourite two clubs in the Premier League, but listed the latter as his preferred destination.
"Playing in the Premier League is a dream for me," he told FourFourTwo.
"I would like to play for two or three clubs, and Manchester United are one of those clubs. But probably not in the next few years – later, when my English is a little bit better! I'm very comfortable at RB Leipzig, though.
"Manchester United and Liverpool were the teams I watched quite a lot in England. They were the two that I'm a little bit a fan of, because they have so much history. When Alex Ferguson was the coach, United won everything and were outstanding.
"I'm now at a point where at some stage in the future I'd like to play in a team that wins titles."