This is according to the latest speculation from talkSPORT, who report that Tottenham are now firmly in the race to sign the Brazilian and that chairman Daniel Levy - a notoriously driven and stubborn character in the transfer market - has even suggested a player-plus-cash deal that would see Luis move to White Hart Lane rather than Stamford Bridge.
Tottenham to secure new left-back?
Tottenham are believed to be in the market for a new left-back, with Cameroon international Benoit Assou-Ekotto having largely failed to impress during a season-long loan spell with recently-promoted Queens Park Rangers, Danny Rose having been to subject to frequent criticism during the 2013/14 campaign and Jan Vertonghen obviously more comfortable in the centre of defence.
A bid for Luis must be deemed as extremely ambitious, however, especially considering the role he played for a team that secured the La Liga title and progression through to the final of the Champions League in hugely impressive fashion last year.
In pursuing such a transfer, one can only presume that Tottenham and new manager Mauricio Pochettino must believe that they have a player to include in part-exchange that will be of significant interest to Atletico and Diego Simeone.
While the identity of the current Spurs man offered by Levy is not revealed, the immediate name that springs to mind is Spanish international striker Roberto Soldado.
The 29-year-old has been linked with Los Rojiblancos in recent months and could relish the chance to return to his homeland following an extremely disappointing maiden Premier League season in which he certainly did not live up to his hefty price tag after making the switch from Valencia.
Indeed, whether Atletico still hold an interest in pursuing Soldado to fill the void left by Diego Costa after today completing the signing of Mario Mandzukic from Bayern Munich remains to be seen.
Watch: The latest Chelsea transfer news
News of Tottenham's sizeable interest in Luis appears to be another complication to Chelsea's attempts to complete a deal of their own.
The well-documented departure of former England stalwart Ashley Cole following the expiration of his contract has left Jose Mourinho slightly short of credible long-term options on the left-hand side of defence, with Ryan Bertrand unlikely to be afforded the opportunity to cement a starting berth on a regular basis and Cesar Azpilicueta perhaps looking to return to his natural position at right-back.
Luis - a rampaging, attacking presence whose initial disappointment at being excluded from Brazil's 23-man squad for this summer's World Cup probably turned to sheer relief following Tuesday's humiliation at the hands of Germany - would appear to fit Mourinho's criteria perfectly, although he is not as strong defensively as Cole.
With a £19 million release clause included in his current contract at the Vicente Calderon, both Chelsea and Tottenham will be aware of the price it will take to prise him away from Atletico.
The former's initial reluctance to meet that particular clause could hand Tottenham an advantage, although it must be considered unlikely at this stage that Luis himself would view them as a particularly attractive transfer destination.
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