The Daily Mirror are often wrong when it comes to transfer rumors, but when it comes to contract renewals, they tend to be pretty reliable, if perhaps a bit premature, in general. So when they report that Chelsea want to give Diego Costa a new contract extension, we can surmise that the Blues have indeed set such wheels into motion, though it might be a while yet before we see some tangible results.
Nine appearances short of a century for the club, Costa is halfway through the five-year deal he signed in the summer of 2014, so it's the proper time to start these negotiations. Add in the constant rumors about a return to Spain and Atlético Madrid and it's doubly imperative that Chelsea retain control and leverage.
Given Costa's form and his own admission that a return had been close before, any extension would likely entail a decent raise as well. With 46 goals so far in his Chelsea career, that's probably a fair deal for all involved.