Adams has a relegation release clause contained in his contract at Elland Road and has been widely expected to depart Leeds at some point this summer.
Though the American midfielder was unable to help Leeds avoid relegation from the Premier League, his stock has remained high.
Now Chelsea are stepping up their interest in Adams and it is claimed to be increasingly likely he will move to the capital.
The release clause is set at in the region of £20m.
Adams has also been linked with other Premier League sides, but it appears Chelsea will win the race.
The Blues are looking for midfield reinforcements and see United States international Adams as a good signing.
Leeds signed Ethan Ampadu earlier this summer and it remains to be seen if he is viewed as the replacement for Adams, or whether the Whites go back into the transfer market.