Luis is said to have a buyout clause of approximately €24 million but Chelsea appear unwilling to pay such a figure, whilst the request is said to have gone down poorly with the hierachy at the Vicente Calderon as they would like to get the best possible deal for the 28-year-old Brazilian.
The defender has already turned down a new contract offer in order to get his desired move but last season's Champions League finalists appear to be taking the view that nobody leaves unless the asking price has been met.
Chelsea have been linked with Luis for much of the summer as he seems to be viewed as the ideal replacement for Ashley Cole at Stamford Bridge. Cesar Azpilicueta was the preferred left-back for Chelsea for much of last season ahead of Cole.
If he were to join Chelsea, he would be the fourth member of the Atleti side that won the title last season to head to West London. Thibaut Courtois looks likely to be recalled after his lengthy loan spell in the Spanish capital. Tiago is said to have agreed a return to Stamford Bridge whilst striker Diego Costa is on the verge of signing for the Blues.