According to German weekly Sport Bild [via Sky Sports], the Ghana international is on the brink of completing his transfer to the west London giants having passed his medical with the club on Thursday.
It was reported earlier in the week that Chelsea had agreed a £20m deal with the Bundesliga outfit. It is said that £14m will be paid upfront with a further bonus of £6m if Rahman makes over 100 appearances for the club.
While Azpilicueta is the undisputed first-choice in this position, any injury to the Spaniard would prove worryingly problematic.
Rahman may therefore be heading to Stamford Bridge simply as back-up – and an expensive one at that – but could be a crucial signing for the reigning Premier League champions.