New Blues owner Todd Boehly has identified Edwards as the man to run their transfer work after axing Petr Cech and Marina Granovskaia.
The Daily Mail says Edwards, however, made it clear when he quit after a decade at Anfield that he planned to take a break for up to a year to refresh and recharge before embarking on his next challenge.
Ideally, Chelsea want someone in position next month so this represents the first obstacle to overcome. The second concerns the degree of control they are prepared to grant the first sporting director of the Boehly and Clearlake Capital era.
Boehly also met with Atletico Madrid sports chief Andrea Berta in London in May about the position.