According to sources quoted by Reuters, there are doubts that Iliad will be able to come through with a more attractive offer.
T-Mobile US has set the French company a deadline of mid-October to improve its offer of $33 a share to take a 56.6% of the company.
Deutsche Telkom is still open to the sale, according to sources, but an improved bid from Iliad now rests on whether it can find suitable investors to help fund the bid.
T-Mobile US continues to represent a growth entity for the European group, and it is thought that some executives at the company are open to holding the unit until a major US radio spectrum auction is completed next year.