The Blues are preparing to back boss Thomas Tuchel in the transfer market this summer after he delivered the Champions League and a top four Premier League finish.
Tuchel is an admirer of former Borussia Dortmund midfielder Weigl, who is on the books at Benfica, and Chelsea have been linked with wanting him.
And in a boost for Chelsea, according to French outlet Foot Mercato, Weigl will be allowed to move on by Benfica if the price is right; he has a release clause of €100m in his contract.
However, there is competition for Weigl with three unnamed clubs keen.
A club from the Premier League are big fans of Weigl and could swoop for him, while a club from the Bundesliga that have qualified for the Champions League are also interested.
From France, a club have lodged an enquiry about Weigl as they seek to test the water.
Weigl clocked 28 appearances in the Portuguese top flight for Benfica this season and picked up a substantial ten bookings along the way.