The Brazil international posted the image of the pair of them side-by-side alongside the caption: "Parceiro colombiano" - or "Colombian teammate" in English.
Speculation claiming Luis could leave Stamford Bridge at the end of the season has intensified over recent weeks, while the jury is out over Cuadrado following a less than convincing start to life with the Premier League title favourites - but both men appear happy and content judging by this latest post.
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Atletico keen to re-sign Luis
It's believed Atletico Madrid would be keen to bring Luis back to the Vicente Calderon if the South American attempts to force a move away from Stamford Bridge, after just one season, this summer.
Reports in February claimed Luis, 29, had told his former Atletico teammate Joao Miranda that he wants to return to Spain after failing to secure a first-team place with his current employers.
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Azpilicueta ahead of Luis
Chelsea forked out £15.8 million to sign Luis last July, but Jose Mourinho has kept faith with the left-back who took Ashley Cole's position last season, Cesar Azpilicueta.
Luis has only made seven Premier League starts this season and is not expected to displace the reliable Azpilicueta before the end of the campaign, increasing the chances of a summer move back to Spain.
Cuadrado has found himself in a similar situation since his £23.3 million move to Fiorentina at the beginning of February.
The Colombia international has only made two Premier League starts for the Blues, with Mourinho preferring Willian instead.
Some Chelsea fans fear Mourinho has signed a dud, but there's little doubt Cuadrado possesses the talent to succeed in the Premier League.
The 26-year-old was superb at Fiorentina and showcased his class at last summer's World Cup finals in Brazil.
But Cuadrado would have signed for Chelsea under the impression he was set to become a first-team regular rather than a squad player - and this is not the case right now.
It's possible that Mourinho is bedding in Cuadrado slowly and will use the lively South American winger on a more regular basis from the start of next season.
But there are plenty of Chelsea fans who feel Willian deserves his place in this Chelsea line-up.
Chelsea fans: are Filipe Luis and Juan Cuadrado good enough for the Blues? Have your say in the comments below!