Chelsea aim to appease frustrated Mourinho with £30m Stones bid
Rahman is expected to undergo a medical after Chelsea finally agreed a an initial fee of £14m, that could rise depending on appearances, with German club Augsburg, while the latest Stones offer is £30m.
Although Everton are unlikely to accept £30m for Stones, Chelsea hope the bid will at least open a dialogue aimed at concluding a deal.
Mourinho had wanted his squad finalised by the start of the new Premier League season, but negotiations over Rahman and Stones have proved to be complicated and drawn out.
Other than the comparative lack of incoming business that Chelsea hope to address, Mourinho has cut a frustrated figure over the club's medical department and issued a public telling-off to doctor Eva Carneiro after the 2-2 draw with Swansea City.
It is not just Carneiro who has been on the receiving end of Mourinho's annoyance, however, as goalkeeping coach Christophe Lollichon has also had his work questioned behind the scenes.
Carneiro's decision to try to treat Eden Hazard in stoppage time, as 10-man Chelsea held on for point, was criticised by Mourinho who this summer claimed the work of his medical department needed to improve.
In a rare Facebook post, Carneiro responded by writing: "I would like to thank the general public for their overwhelming support. Really very much appreciated."
Lollichon was expected to follow Petr Cech to Arsenal during the summer and the Frenchman may yet end up at the Emirates as his relationship with Mourinho is not particularly close.
While Mourinho has kept any words of displeasure with Lollichon private, the decision to publicly question Carneiro's work came as a surprise.
Given Chelsea had one of the best fitness records in the Premier League and captain John Terry played every minute of every game last season, Mourinho's frustration appears to stem from Diego Costa's hamstring problems.
Mourinho was advised that Costa did not need surgery on the injury at the end of last season, but the striker was unavailable for the Community Shield and missed the final pre-season friendly against Fiorentina.
Costa was fit to start against Swansea, but another season of hamstring difficulties may well see Mourinho question, either privately or publicly, the decision for him not to be operated on. Carneiro is a highly respected figure within Chelsea and is very highly rated for her work by the club's players.
Her skills may be quickly put to the test again after Chelsea decided to appeal against the red card Courtois was shown against Swansea. Chelsea want Courtois to be available for selection for the trip to Manchester City on Sunday, even though he is carrying a knee injury that he suffered in the warm-up for the Swansea game.