Liverpool and Barcelona are among the clubs to have been most heavily linked with a bid for Werner but the lure of Old Trafford still seems strongest for the 21-year-old, who grew up watching years of success under Sir Alex Ferguson.
"As a young boy, you always dream of the big club you'd like to play for," he told Sky .
"It used to be Manchester United under Alex Ferguson, who always won. A young boy is always a fan of those who win.
"You can't just drop something like that. When it's going well, you dream of playing somewhere else."
In the shorter term, Werner is confident Leipzig can challenge for silverware this season, with Raplh Hasenhuttl's side just three points behind league leaders Borussia Dortmund despite the added commitment of Champions League football.
"We want to win some trophies," he said. "I don't know if this will happen with RB but the chances are good this year that we can get a trophy."