With Real Madrid seemingly set to confirm the signing of Eden Hazard for £88million in the coming days, Blues fans would have hoped the cash could be spent improving the squad.
FIFA had banned the Premier League side from signing players in February for the next two transfer windows after being found guilty of 29 breaches of regulations over transferring minors.
The governing body then rejected an appeal from Stamford Bridge last month, with a follow-up appeal then lodged to the CAS in Switzerland.
But the west Londoners may not make another signing now until next summer.
A CAS spokeswoman told Sun Sport on Friday morning: “For a challenged decision to be stayed during the CAS proceedings, a specific request to this effect must be made.