The 24-year-old followed compatriot and former manager Jesse Marsch to Elland Road last summer, leaving RB Leipzig in a €17m (£14.7m) deal.
Adams was often a shining light in a troubled season for Leeds, making 26 appearances in all competitions and starting 24 games in the Premier League.
However, the USA international suffered a season-ending hamstring injury in March, and he helplessly watched on as the Whites won just two of their final 12 games of the campaign to drop back down to the Championship.
Adams missed Leeds' opening 2-2 draw with Cardiff City at the weekend as he continues his recovery, and the midfielder is still under contract at Elland Road until the summer of 2027.
Adams may not be sticking around in Leeds for much longer, though, as according to the Daily Mail, the midfielder has a clause in his deal allowing him to leave for £20m in the event that the Whites were relegated.
Chelsea have supposedly shown a willingness to pay that fee and are ready to trigger Adams's clause, as Mauricio Pochettino seeks further reinforcements in the middle of the park.
The report adds that Adams does not intend to be playing Championship football for the 2023-24 campaign, and Chelsea are hopeful of sealing a deal before this weekend's Premier League opener versus Liverpool.
The Blues may still have to fend off late threats from Aston Villa and other unnamed top-flight rivals, but Adams is thought to have earmarked Stamford Bridge as his preferred destination.
Chelsea have parted ways with a number of long-serving midfielders in 2023, allowing Jorginho, N'Golo Kante, Mateo Kovacic, Mason Mount, Ruben Loftus-Cheek and Tiemoue Bakayoko to seek pastures new.
Conor Gallagher's long-term future remains unclear too, and the 23-year-old has been the most experienced lynchpin available to Pochettino in pre-season, linking arms with Enzo Fernandez, Carney Chukwuemeka, Andrey Santos and Cesare Casadei in the middle.
The Blues have added to their engine room with the capture of teenage starlet Lesley Ugochukwu from Rennes, but the 19-year-old is expected to be loaned out to Strasbourg for the upcoming campaign.
Brighton & Hove Albion's Moises Caicedo remains Chelsea's top target in the engine room, and the Blues are understood to be lining up a fresh approach from the Ecuadorian, despite failing with a bid of £80m last week.
Should Brighton continue to rebuff Chelsea's advances, Paris Saint-Germain outcast Leandro Paredes has apparently emerged as an alternative option to the 21-year-old.
Robert Sanchez, Diego Moreira, Angelo Gabriel, Axel Disasi, Nicolas Jackson and Christopher Nkunku have also touched down in West London this summer, but the latter could miss the start of the new season with a knee injury picked up during the Blues' pre-season tour of the USA.