Chelsea have not conceded in three games since the 3-0 loss at Roma, after which boss Antonio Conte dropped Luiz, one of the cornerstones of his Premier League title-winning team.
Denmark defender Christensen slotted in seamlessly in a 1-0 win over Manchester United and kept his place for last Saturday’s 4-0 victory at West Brom.
Brazil defender Luiz returned for Wednesday night’s 4-0 win at Qarabag, which secured Chelsea’s place in the last 16 of the Champions League, giving Conte a decision to make for Saturday’s trip to Liverpool.
“David came back in and performed well,” Cahill said.
“Andreas is a younger version of him if you like. I feel like David can offer Andreas a lot of help in his progression.
“He has been there and done it at the top, top level, he has won many trophies.
“David is a very experienced defender and Andreas’ attributes are very similar. I feel that he (Luiz) can advise him tremendously and he has done up until now.”
Chelsea advanced ahead of December’s clash with Atletico Madrid, who beat Roma to maintain their slim chances of progressing from Group C.
“The aim was to get through from the start of the campaign,” Cahill added.
“It is a good achievement. We are happy, we knew we had to win. We didn’t want to leave it until the last game, for what will be a very difficult game.
“It does alleviate the pressure against Atletico. We have a job to do in a fortnight, but beating Qarabag has taken some of the edge off.”
Conte, meanwhile, is ignoring Liverpool’s inconsistencies ahead of the trip to Anfield.
The Italian immediately turned his attention to Liverpool on the five-and-a-half-hour flight home from Baku to London, which landed at Gatwick at 0300GMT on Thursday.
Jurgen Klopp’s men have an additional 24 hours of preparation following their 3-3 draw at Sevilla on Tuesday, when they had led 3-0 at half-time.
“I watched the game and I think Liverpool played a really good first half with great intensity and they scored three goals,” Conte said.
“Football is strange. What happened in the second half is very difficult to explain.
“Liverpool also in the second half had opportunities to score other goals. In the second half they were also unlucky.”
Conte has railed against the perceived injustices of the Premier League fixture schedulers.
Chelsea won at Atletico on a Wednesday night in September before playing Manchester City the following Saturday. City had played at home in Europe on the Tuesday evening and won 1-0.
And Conte, whose side now trail City by nine points, is frustrated that a similar scenario has occurred.
He is now focused on getting the most out of his players from limited preparation.
The Blues had a recovery session scheduled on Thursday before Friday’s pre-match training session.
Victor Moses, who spent the 2013-14 season on loan at Liverpool from Chelsea, could return to contention following a hamstring injury.