According to the Daily Mail, Chelsea boss Jose Mourinho is ready to sanction a cash-plus-player deal to bring Costa to Stamford Bridge.
But rather than Thibaut Courtois, the highly-rated young goalkeeper on loan at the Vicente Calderon from Chelsea, the report claims Mourinho will offer Diego Simeone the chance to sign Romelu Lukaku instead.
Spurs have recently been linked with Costa, who has helped fire Atletico Madrid into the La Liga title race this term.
Tottenham chairman Daniel Levy has grown impatient with the lack of return from big-money signing Roberto Soldado.
And he's prepared to back Tim Sherwood in the transfer market this summer. Costa, valued by Atletico in the region of £40m, has emerged as a potential target for Spurs, who still have spending power following the summer departure of Gareth Bale to Real Madrid.
Despite the fact that Chelsea remain favourites for Costa, a potential lifeline for Tottenham in their pursuit could be found in Radamel Falcao.
The report notes Chelsea owner Roman Abramovich is still a huge fan of the Colombian international and even though he's injured, the Blues may look to sign him this summer instead of Costa if he proves his fitness.