The optimism emerged with news that powerful Hamas politburo chief, Khaled Meshaal, was expected soon in Egypt for talks on the matter with Egyptian officials who have been the main broker in the crisis.
The soldier's release is linked to "Israeli responses to Palestinian demands and I think there is progress as the Egyptian brothers told us. They are the ones following the matter," Haniya told AFP after Friday prayers.
Nevertheless the premier, head of the Hamas-led government boycotted by Israel and the West, said he had no details about Meshaal's visit to Cairo.
"There is no more information on Khaled Meshaal's visit but contacts with the Egyptian brothers have not been interrupted," he said.
Hamas has demanded the release of some 1,000 Palestinians held in Israel in exchange for Corporal Gilad Shalit, whose capture sparked a prolonged Israeli offensive in Gaza where more than 250 Palestinians have since been killed.
An Israeli cabinet minister earlier expressed cautious optimism about the prospect of securing Shalit's release. He was seized in June by Gaza-based militants, including those from the armed wing of Hamas.
"Being aware of all the details concerning this affair, I prefer to keep quiet. I became optimistic during my recent visit to Cairo and that I remain," Infrastructure Minister Benjamin Ben Eliezer told army radio.
Ben Eliezer, a member of Israel's weighty security cabinet, met Egyptian President Hosni Mubarak and intelligence chief Omar Suleiman, a key negotiator for the soldier's release, in Cairo on October 19.
"All I can tell you, is that I greatly thank President Mubarak and General Suleiman," Ben Eliezer added.
"I went to Cairo with the feeling that the Egyptians, on this matter, had an obsession: to finish. That's what I told Noam Shalit, the father of the soldier, upon my return," the minister said.
In Gaza, a Hamas spokesman said an agreement on a prisoner swap was almost ripe and that Meshaal was expected to go to Cairo soon to meet Egyptian officials with a view to an agreement on Shalit.
"I think that an agreement is almost ripe and that Khaled Meshaal's visit to Cairo is concrete proof of that," Fawzi Barhum told AFP.
"Israel has agreed to release (Palestinian) prisoners in exchange for the Israeli prisoner after having refused and having wanted Shalit's release without conditions," Barhum added.
Nevertheless Barhum denied Israeli reports that Meshaal -- declared a marked man by Israeli officials for allegedly ordering Shalit's capture -- would go to Cairo as early as Saturday.
"Khaled Meshaal will go to Cairo soon but so far no date has been fixed," he said. "It's Khaled Meshaal who has the last word because he knows the case in detail," the spokesman said.
Barhum reiterated that Hamas wanted leverage over which Palestinians would be released, such as members of various factions jailed for longer than 10 years. These include Marwan Barghuti, Jamal al-Natsheh and Ahmed Saadat.
"This question is currently the object of talks between Egypt and the Israelis," he said.
Israel has previously rejected demands that Barghuti and Saadat, two militant leaders, be released in return for Shalit.

Copyright AFP (Agence France-Presse), 2006