The 25-year-old has been superb and has looked worth every penny of the £32 million transfer fee that Chelsea had to pay Atletico Madrid earlier this summer for his services.
However, Mourinho is in the market for another striker due to the departure of Fernando Torres to AC Milan on a two-year loan deal.
Queens Park Rangers star Loic Remy is widely reported to be the Portuguese’s main target in the final days of the summer transfer window, and former Liverpool striker Stan Collymore believes that the France international will form a lethal partnership with Costa if Mourinho plays two up front.
I think Costa AND Remy could work together. Jose like his 1 up top but if he's flexible, could be a cracking partnership! @SportsYapper— Stan Collymore (@StanCollymore) August 30, 2014
However, Chelsea are not the only club interested in Remy. Arsenal are also looking for a striker due to a recent injury picked up by Olivier Giroud which is expected to keep him out of action until the New Year.
Remy failed a medical at Liverpool earlier this summer, but the interest in him from Chelsea and Arsenal means that the 27-year-old could still play for one of the biggest clubs in England this season.
And Collymore, who now works as a football pundit, believes that Remy is spoilt for choice.
Both Chelsea and Arsenal set up with lots of ammo for a front man, so Remy is a luck boy and in a great bargaining position. @SportsYapper— Stan Collymore (@StanCollymore) August 30, 2014
It will be interesting to see what Remy does. As Collymore correctly points out, at Arsenal he is certainly going to get more games, but working with Mourinho and having the chance to win a number of trophies could prove to be too tempting to resist.