The 36 year old is currently a free agent having spent the last eighteen months with Turkish giants Galatasary, and the Blues are leading the race to secure his services.
During his first spell with the club, the Ivory Coast international made three hundred and forty-one appearances in all competitions, scoring one hundred and fifty-seven goals on route to collecting a whole host of major honours.
His success culminated in the 2012 Champions League triumph in the Allianz Arena, where his penalty secured victory in the penalty shoot-out against Bayern Munich.
Should he return to Stamford Bridge, he is likely to do so as a player-coach and he could make his second Blues debut against Burnley in next month’s season opener.
Jose Mourinho’s men are favourites to win the Premier League next season at a price of 15/8.