Luis is unhappy at Stamford Bridge and has been linked with a return to Atletico Madrid this summer, although Inter Milan are also said to be interested.
That will leave Jose Mourinho looking for a replacement and Ghana international Rahman is reportedly on the Portuguese manager's radar.
But according to the Evening Standard, Arsenal and Manchester City are both also interested in the 20-year-old.
Chelsea are said to have made a £10.6million bid but Augsburg are holding out for closer to £15m for their prize asset.
Rahman is currently on holiday back in his native Ghana, but is thought to be keen on a move to a Champions League club this summer.
And both player and club want the matter sorted out before the start of pre-season begins at the start of next month.
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