The 23-year-old striker is set to sign for Chelsea in a £54 million deal later this month and is ready to give up a shot at European glory with the German side so he can move to the Blues.
According to Bild newspaper, the German forward is determined to be in London by July meaning that he will miss out on the conclusion of Europe's top competition.
The Champions League looks set to be concluded in a mini-tournament held in Portugal in August, with Lisbon likely to host the matches.
RB Leipzig have already progressed to the quarter-finals but Chelsea face elimination after a 3-0 defeat to Bayern Munich in the first leg of their last 16 tie before football was suspended across Europe.
It is claimed that Werner has been removed from Leipzig's Champions league squad and there is a "high probability" that Frank Lampard's side will activate his release clause.
He is one of the highest-rated strikers in Europe and has also been linked with moves to Liverpool and Bayern Munich before settling for Chelsea.
The London club have also made Bayer Leverkusen winger Kai Havertz and Leicester City defender Ben Chilwell transfer targets. They are seeking to make early moves as other clubs weigh up how much to spend amid the coronavirus pandemic.