"We have received an offer, via intermediaries, for a prisoner exchange," a source with the Ezzeddin al-Qassam Brigades told the Qatar-based Al Jazeera television channel.
The source, whose name was not disclosed by the channel, said the offer had failed to meet the group’s "minimum demands".
There has been no official comment by the Israeli government regarding the group’s assertion.
On Monday, however, an Israeli official was quoted by The Times of Israel news portal as saying that the Israeli government had extended an offer to Hamas via international mediators.
Last year, the Qassam Brigades said it was holding four captured Israeli soldiers, declining to give any further details as to whether or not they were alive.
The Israeli government admits it lost track of two soldiers during its 2014 military offensive against the Gaza Strip.
Israel has also said that two Israelis had gone missing after illegally entering the Gaza Strip, which has been governed by Hamas since 2007.
In 2011, Hamas and Israel carried out an Egypt-sponsored prisoner swap under which Israeli soldier Gilad Shalit was released in return for 1,027 Palestinian prisoners held by Israel.
The Israeli authorities later re-detained 60 of the Palestinians freed in the swap.
There are around 7,000 Palestinian prisoners currently being held in Israeli jails, according to Palestinian estimates.