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Israel has offered to remove the economic embargo on Hamas if kidnapped IDF soldier Cpl. Gilad Schalit is freed and Kassam rocket attacks stop, the London-based Arabic newspaper Al-Hayat reported on Sunday morning.
The message was reportedly conveyed to the Islamic group via Arab mediators.
A Hamas source in the Gaza Strip was pessimistic about the seriousness of the proposal, telling Al-Hayat that it was an Israeli attempt to "put out the feelers" on the now Hamas-controlled Gaza Strip.
He said that Israel had proposed a removal of the embargo, which has been in place since the Palestinian Legislative Council elections in January 2006, allowing the delivery of merchandise to Gaza.
However, according to the report, Israel remained steadfast in its refusal to transfer frozen tax revenues or other funds in exchange for Schalit.
On Thursday, diplomatic sources said that in light of the current infighting in Gaza between Fatah and Hamas, the frequency of negotiations over Schalit's release had gone down.
According to the sources, contacts between Hamas and Egypt - who has been serving as mediator between Hamas and Israel - would only resume once the situation in Gaza stabilized.
Meanwhile, the Hamas source added that kidnapped BBC reporter Alan Johnston would be freed by this weekend. He said that the kidnappers, who belong to the Durmush clan, recently contacted Hamas, who threatened that if Johnston were not released within 48 hours Hamas would use force.
Another Hamas official said that Johnston, who has been held since March, would be freed soon.
"All I can say is that Alan will be free very soon," Islam Shahwan, spokesman for Hamas in Gaza, said Sunday.
However, Hamas spokesman Sami Abu Zuhri, downplayed hopes for his quick release, saying, "there is nothing new yet regarding Alan."