Many supporters expressed their discontent at the former Liverpool boss replacing Roberto Di Matteo at the Champions League-winning club but since the Blues moved to within seven points of second place in the Premier League table, Le Saux believes that the tide is turning.
"The relationship between the fans and club is building again," London 24 quotes Le Saux as saying.
"The fans were very quick to show their frustration at Roberto Di Matteo being sacked, but I think over time they are warming to the change. Ultimately the results we get as a club will dictate how the crowd respond."
Meanwhile, the Blues are preparing to face Stoke City at the Britannia Stadium this Saturday.