The striker has been most frequently linked with Liverpool and has previously expressed his admiration for Jurgen Klopp.
The 24-year-old believes joining the Premier League leaders or City would represent a good opportunity to play for a strong side under a "great" coach, although he appears tempted by the idea of Ole Gunnar Solskjaer's project to turn United back into England's dominant force.
However, Werner has not ruled out staying at Leipzig, where he thinks he could "make something great".
Speaking ahead of his side's Champions League last-16 second leg against Tottenham, he told Sky Sports: "At this time in professional soccer, there are two different variations.
"The first is to be part of a team like Liverpool or Manchester City. They have a good working team. The teams have also great coaches.
"But this is the question: do you want to go to that kind of team, because the situation is already that hard for each member and you want to be a part of it? That's one point you have to look at.
"The other side are teams which need some big changes, because they just won a few big titles, but they are not able to compete on the highest level anymore. For me, Manchester United is one of these teams.
"So at this point of my career I'm asking myself: do I want to be part of a new team, to build up something new, or do I want to stay at my team and make something great?"
Werner has scored 27 goals in 35 appearances in all competitions this season.
He is second only to Robert Lewandowski in the Bundesliga goalscoring charts this season and converted the second-half penalty at Tottenham Hotspur Stadium to secure Leipzig's first-leg lead over Spurs.