Both London clubs have been linked with a move for the Brazilian born striker, who has been scoring goals for fun in La Liga this season.
But Atletico Madrid president Enrique Cerezo has revealed he has no intention of selling the club’s prized asset, adding that he believes the club are in a different position as to when they sold Radamel Falcao to Monaco last season.
Jose Mourinho’s Chelsea were thought to be the favourites for Costa’s signature, with on loan goalkeeper Thiabut Courtois mentioned as being used in a possible part-exchange deal.
But Cerezo is not thinking about such a move, and believes Costa can be convinced to stay in the Spanish capital.
“I do not think Diego Costa will leave us at the end of the coming year,” Cerezo said.
“Unquestionably, we do not want to sell him or use him as a bargaining chip for another player.
“We will never sell, but that won’t stop teams coming in for our players.”
Costa is believed to have a £32million release clause in his contract, which would leave Atletico obligated to allow the forward to negotiate with another club should the figure be met.