After the sale of Filipe Luis back to Atletico Madrid, the Blues are in the market for a left-back and have targeted the Ghana international.
With Rahman keen to get the deal over the line, his agent, Sascha Empacher, says that personal terms are all set as the teams negotiate.
He told Sport Bild: "It is only the clubs that have to find an agreement. We on our side are agreed."
Empacher had earlier confirmed on Friday that Chelsea had "made an attractive offer" to the 21-year-old.
Augsburg appeared to line up a replacement for Rahman on Tuesday, signing left-back Philipp Max from Karlsruhe.
