The Brazilian – who helped the Rojiblancos to claim the Spanish title last term – is understood to be Jose Mourinho’s top target to replace Ashley Cole at Stamford Bridge, with contact having been made between the player and the London club.
However, reports suggest that Spurs are also in the running and are ready to attempt an audacious hijack.
The 28-year-old is rumoured to be ready to join the Blues, but the White Hart Lane outfit are hopeful that he can be persuaded to choose the north end of the capital over the west.
Chelsea have displayed a reluctance to meet Luis’ £19m release clause, which is thought to have angered Atleti – who have already lost star striker Diego Costa to them.
Tottenham’s valuation is also short of the Spaniards’ demands, but Mauricio Pochettino is ready to compromise with a player plus cash deal.
Roberto Soldado is one Lilywhites star to have been linked with a move to the Vicente Calderon.