Fallows is expected to work closely with Chelsea's sporting directors, Paul Winstanley and Laurence Stewart, as well as the co-directors of recruitment and talent, Joe Shields and Sam Jewell.
His responsibilities would include scouting, player development pathways, and football development, a different role to the one he held at Liverpool.
Fallows left the Anfield club in October 2024 after spending 12 years on Merseyside.