New owner Todd Boehly has been the club's interim sporting director after Marina Granovskaia resigned from the role in July.
In their search for Granovskaia's replacement, Chelsea are believed to have drawn up a four-person shortlist of suitable candidates.
According to the Daily Express, the shortlist contains former Barcelona full-back Maxwell and former Liverpool sporting director Michael Edwards.
However, there are reports that following a 10-year association with Liverpool, Edwards is looking to take an extended break away from football.
Paul Mitchell, who is currently working at Monaco, is believed to be another candidate, while the fourth individual on the shortlist is not currently known.
Boehly is keen to appoint a new sporting director in time for the January transfer window.