The Izz ad-Din al-Qassam Brigades said it received Israeli offers to make a prisoner exchange deal.
According to Al Jazeera, the Brigades stressed that the "the format suggested by Israel did not address the least of our demands."
Al-Qassam announced for the first time last April that it captured "four Israeli prisoners", but did not reveal formally whether they were alive or dead.
It has continuously refused to provide any information regarding the Israeli soldiers captured. It also refused to reach a new prisoner exchange deal before Israel releases the Shalit exchange prisoners who have been re-arrested.
Analysis: Prisoner swaps between Hamas and Israel are a sensitive issue
A spokesman for the Qassam Brigades, Abu Obadiah, announced on 20 July 2014, during the Israeli attack on Gaza, that the Brigades captured Israeli soldier Aaron Shaul, while they were fighting off an Israeli ground raid in the Al-Tuffah neighbourhood located east of Gaza City.
The Israeli government had previously announced the loss of the bodies of two soldiers in the Gaza Strip, Aaron Shaul and Hadar Goldin, during the Israeli war, which began on 7 July 2014 and ended on 26 August 2014. However, the Ministry of Defence recently classified them as missing and captured.