The Brazilian-born Spain international is expected to leave the Champions League finalists and La Liga leaders on the back of an impressive season, with the Blues having been his most likely destination for some time.
Rumours have suggested that a deal for the 25-year-old to relocate to the west end of London has been all but sealed for some time, but now it appears that Arsenal are also in the running.
Arsene Wenger sees Costa – who has a £31m release clause in his contract – as a good option to lead his line after relying heavily on Olivier Giroud this term.
The Atletico goal-getter’s fee should not be too much of an issue for the Frenchman who was willing to pay £40m for Liverpool star Luis Suarez last year.
Chelsea still remain in pole position for the striker, with the Stamford Bridge side said to be willing to pay him a huge salary to solve their forward issues.