The Blues are one of a number of clubs reportedly interested in signing Colombia striker Falcao, who has scored 10 goals for Atletico Madrid this season.
With Fernando Torres still struggling to find the form he displayed during the peak period of his Liverpool career, Falcao could be just the player the Blues need to boost their Barclays Premier League title bid.
The 26-year-old is thought to have a hefty release fee clause in his contract, but Luiz thinks Chelsea would be an ideal destination for the player.
"He would fit perfectly in to the squad," Luiz told Brazilian media after the country's draw against Colombia in the United States on Wednesday night.
"We would all be happy (if he signed) because Falcao would undoubtedly a great player for our team."
Luiz said of Falcao, according to Terra.com: "He is very difficult to stop. He is an excellent striker."
The Blues have also been linked with a bid for Juventus' Stephan Lichtsteiner, but his agent played down talk of the Swiss right-back moving to Stamford Bridge.
"I don't know where these rumours come from," his agent and father Marko Lichtsteiner told calciomercato.it.
"Stephan is happy at Juventus: they are first in the league and we hope they get through the (group) round in the Champions League.
"He wants to stay, he has no intention of leaving Turin and there is no reason to do it.
"He has no problems with (the coach). They are two people who have a strong characters and always want to win.
"If the club has other ideas for Stephan, I don't know."
The Blues will hope to add spark to their title push on Saturday when they travel to high-flying West Brom.
The Londoners will be without John Terry for the match as he continues his recovery from the knee injury he suffered against Liverpool last weekend.
Chelsea have been conducting tests on their captain's injury this week in the hope of determining exactly how long he will be sidelined for.
Manager Roberto Di Matteo is expected to give an update on the defender's condition, and that of injured duo Ashley Cole and Frank Lampard, at his weekly press conference on Friday.
Meanwhile the agent of Fluminense defender Wallace has claimed Chelsea are on the verge of signing the 18-year-old Brazilian.
His representative Frederico Moraes told Italian radio station Centro Suono Sport: "There are very advanced negotiations with Chelsea and the signature is almost certain.
"If Wallace goes to Chelsea, he will be playing there.