According to a new Bloomberg report, French telecom firm Iliad is apparently mulling a second bid for the acquisition of US wireless carrier T-Mobile.

Iliad's second bid for T-Mobile would essentially mark a sweetening of the French carrier's first offer made to T-Mobile's parent company, Deutsche Telekom, in July this year. In that offer, Iliad looked to acquire a 56.6 percent controlling stake in T-Mobile at $33 per share.

However, Deutsche Telekom - the German telecom giant which currently owns 66 percent of T-Mobile - had turned down that offer.

With Deutsche Telekom executives believing that $35 per share would be a fair asking price for T-Mobile, it is not yet certain whether Iliad's second bid will meet the expected price. Nonetheless, as per the Bloomberg report, Iliad is now considering the purchase of a bigger chunk of T-Mobile, and possibly even take the carrier off Deutsche Telekom's hands.

According to the information shared by Bloomberg's unidentified sources familiar with the matter, the new T-Mobile acquisition offer which Iliad plans to make to Deutsche Telekom will be for a bigger stake at $33 per share. The sources have also revealed that Iliad founder and billionaire entrepreneur Xavier Niel is apparently planning to reach a preliminary agreement with Deutsche Telekom by the end of this month.