The former Blues boss, who presided over a hugely successful spell with the West London club from 2004 to 2007, is the red hot favourite to fill the void left by interim boss Rafa Benitez's exit.
Real Madrid confirmed that the enigmatic Portuguese coach would step down at the end of this season, paving the way for a second stint with Chelsea.
And England centre-back Cahill is keen to work under a manager who many of his team-mates hold in such high regard.
Cahill told Sky Sports News: "I know that he is held in high esteem here, the lads speak highly of him, everyone speaks highly of him, so he must have something about him.
"Any player would relish working under somebody like that and look forward to it.
"If it is that, we don't know, but I'm sure every player would like to work under somebody like that."