The 26-year-old enhanced his reputation throughout the tournament with a string of commanding performances for Portugal, prompting repeated links with a move to Chelsea in recent weeks.
According to TSF, Stamford Bridge is emerging as the most likely destination if Porto are eventually forced into a sale, with the club understood to have been tracking Costa closely even before the World Cup began.
Costa's showings for Portugal have reportedly reinforced Chelsea's admiration for the goalkeeper, with TSF adding that the club's interest has intensified as the tournament has progressed, elevating him to one of their leading priorities for the summer window. New Chelsea manager Xabi Alonso is also said to be an admirer of the Porto captain, according to the report, giving the London club further reason to press ahead with a move.
Porto, though, remain determined to keep hold of their captain. Head coach Francesco Farioli said last month that he hoped Costa would stay, joking that he would "close the airport and the roads" to prevent a departure, while stressing that "FC Porto is his home."
Costa signed a new contract at the Estadio do Dragao before Christmas that runs until the summer of 2030, with the deal including a release clause of €60million (£51million) that gives any interested club a clear route to a deal.
Chelsea are not without competition, with Paris Saint-Germain, Manchester United, Manchester City and Bayern Munich all previously credited with interest in Costa at various points over the past year.
TSF's report, though, suggests Chelsea are currently viewed as the club most prepared to make a serious financial commitment, even amid interest from several of Europe's other heavyweight clubs.
Costa has established himself as Portugal's undisputed first-choice goalkeeper and has made more than 200 appearances for Porto since coming through the club's academy.
Chelsea made an initial approach for Costa last summer that ultimately fell short, with the club instead signing Filip Jorgensen from Villarreal, but their long-term interest in the Portugal captain appears to have persisted regardless.