In this paper, we propose a new delayed data offloading scheme by exploiting full-duplex (FD) device-to-device (D2D) communications. To this end, we consider a scenario in which a common file is requested by a subset of users in different times and with different maximum tolerable delays. Moreover, a maximum specific bandwidth is dedicated for data transmission. In order to send the file in the specific bandwidth, we use multicasting alongside FD D2D communications. Thanks to the fact that users have different deadlines, we divide them into non-overlapping groups, i.e., coalitions, to receive the file in distinct intervals. In order to guarantee the tolerable delay of all users, a coalition formation method is proposed to find efficient cooperation strategy for users. Furthermore, FD communications enables us to schedule multi-hop transmissions at each coalition. To evaluate the performance of the proposed offloading method, we compare the time-integrated bandwidth of our proposed scheme with the case that no D2D communications is permitted.