The Blues had made a surprise approach for the Frenchman on transfer deadline day as Antonio Conte looks to add to his squad.
But, according to Sky Sport Italia, the 28-year-old has turned down the opportunity to head to Stamford Bridge.
Chelsea had been looking to take Biabiany on loan until the end of the season and this is reportedly the cause of the deal's collapse.
The winger, although he is not in Inter's plans, is reluctant to leave on loan and would only be interested in a permanent switch.
As a result, Biabiany has turned down Chelsea's offer and he looks set to stay at the San Siro for now.