The Cottagers have been linked with a move for the 33-year-old centre-back, who has fallen out of favour under Maurizio Sarri at Stamford Bridge this term.
Cahill would be a welcome addition at Craven Cottage, with Fulham having conceded a league-worst 49 goals so far this season.
Ranieri has admitted his side would be very grateful to add Cahill, who has played just seven times for Chelsea this term.
"Gary is a very important player and for us [his transfer] would be fantastic," Ranieri said ahead of his side's game against Tottenham on Saturday.
"I don't know if he wants to come and fight with us."
While Cahill's arrival is still in doubt, one player who is definitely joining Fulham is Ryan Babel, who signed from Besiktas earlier this week.
Ranieri hopes that the 32-year-old's experience from playing at Liverpool earlier in his career can help Fulham as they look to avoid dropping straight back down to the Championship.
"I hope Ryan can bring his experience, his strength, he is a quality player, some goals because we need goals," Ranieri said.
"Of course, I hope he can adapt to our football as soon as possible but I am happy because he played for Liverpool so he knows the Premier League very well."
Fulham are currently 19th in the Premier League, five points adrift of safety.