The London club moved a step closer to that aim on Wednesday when they reached the Women's Champions League semi-finals after a 1-1 draw with Ajax.
Chelsea advanced 4-1 on aggregate after winning the first leg in Amsterdam 3-0.
Hayes will take over the US women's national team at the end of the season - beginning with a bid to win Olympic gold in Paris.
Before that, she is aiming to lift a quadruple of trophies with Chelsea, including the Champions League for the first time.
The Women's Super League champions had effectively secured their place in the next round after a dominant performance in the first leg, and they extended their advantage to 4-0 on aggregate after Mayra Ramirez scored in the 33rd minute at Stamford Bridge.
Chasity Grant scored in the 65th minute to give Ajax some consolation and a 1-1 draw on the night.
While Chelsea are searching for their first Women's Champions League trophy, Ellie Carpenter's Lyon are hunting a record-extending ninth.
The Matildas right-back played a full 90 minutes as the French champions advanced to the semi-finals for a record 13th time after a 4-1 win over Benfica.
Delphine Cascarino and Kadidiatou Diani scored two goals each as record eight-time champions Lyon won 6-2 on aggregate after a 2-1 first leg victory in Portugal.
Lyon last won the trophy in 2022 and will play either Hacken or Calre Hunt's Paris Saint-Germain in the semi-finals.
Chelsea will face either Brann or defending champions Barcelona.
PSG and Barcelona both won their quarter-final first-leg matches 2-1 and will host their respective second-legs on Thursday (Friday AEST).
- with AAP
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