The Portugal international has spent his entire career at FC Porto, and has just won the domestic league title with the club.
Costa was promoted to the senior squad in the summer of 2019, and has gone on to make 246 competitive appearances for the team since then, establishing himself as captain and one of the most consistent performers in Portuguese football.
The 26-year-old has been linked with a move away from Porto for some time, with his performances for both club and country over recent seasons drawing consistent attention from elsewhere in Europe.
He has recently been mentioned in connection with Juventus, as well as Paris Saint-Germain, who could be searching for a goalkeeping upgrade this summer.
According to Mirror Football, Manchester United have a long-standing interest in Costa, but could now find themselves facing competition from another English club.
The reports suggest Chelsea are renewing their interest ahead of the summer, with Xabi Alonso said to be keen to strengthen between the posts following his move to take charge at Stamford Bridge.
Chelsea are reported to be following the Portuguese goalkeeper's situation closely, and according to Portuguese newspaper Record, any deal could carry a significant price tag.
Porto are said to be demanding €60m for the goalkeeper, according to the newspaper.
The reports also suggest that figure could rise further if Costa produces a strong performance at this summer's World Cup with Portugal.
Porto have tied Costa to a contract running until the summer of 2030, and should be under no pressure to sell this window.
Costa's situation echoes a pattern that has followed him for several transfer windows, with his release clause and contract length giving Porto considerable leverage over any potential departure.
Manchester City and Bayern Munich have also been credited with interest in the goalkeeper at various points over the past two years, though neither club has been mentioned in the most recent reporting.
Chelsea's perceived need in goal stems partly from inconsistent performances further down the pecking order at Stamford Bridge, a factor that has pushed the club to widen its search across Europe's leading leagues this summer.
The goalkeeper has established himself as one of the most reliable shot-stoppers in European football, and his performances at the World Cup are likely to play a significant role in determining how the chase for his signature develops over the coming weeks, with several clubs expected to monitor his form closely throughout the tournament before making any final decisions this summer.