Meanwhile, the west London giants have begun pre-season training without the involvement of current boss Antonio Conte and this appears to give a clear indication that the 48-year-old should end his association with the club in the coming days.
The managerial saga has dragged on and on over the course of the summer, with Chelsea players left in confusion having already returned to their Cobham training ground for pre-season training.
Antonio Conte is expected to return to Chelsea to take first-team training on Monday despite uncertainty over his future at the club.
The report claimed that Rugani's arrival is a big hint that manager, Maurizio Sarri is closing in on his move to Stamford Bridge.
Chelsea have alternative options in place should the talks with Sarri collapse, with ex-Paris Saint-Germain head coach Laurent Blanc likely to be the next in line to take charge.
Russian Federation vs. Croatia - Football Match Report
Russia's unlikely run came to an end at the quarter-final stage as Croatia once again progressed via a shoot-out. Russia's Fyodor Smolov took the first kick but it was saved by Croatian goalkeeper Danijel Subasic .
The Brazilian has not played for the club since February after a fall-out with Conte.
It seems he's been offered a fresh start at Chelsea and Sarri could be eyeing the Italian global as a potential replacement for David Luiz with the Brazilian star tipped for a move after falling out of favour last season.
That, after all, is just how the club works.
Conte is also holding out for his £9m and intends to work his past year of his contract unless he gets it, having not had any concrete offers from other clubs and after turning down Italy's interest in re-appointing him.