Hamas has demanded the release of of 1,000 Palestinian prisoners held by Israel in exchange for Shalit.
"They will be released in two stages, al-Mzainy said.
"The first group will comprise 450 prisoners, whose names are determined by Hamas... In the second stage, 550 prisoners will be released. Hamas is attached to this plan.
"We will not accept any deal unless this request is accepted."
Among those that Hamas wants freed is Marwan Barghouti, a popular leader from the rival Fatah movement, a demand that is thought to be one of the stumbling blocks in negotiations.
Barghouti was arrested in the West Bank in April 2002, and is serving five life sentences in an Israeli jail.
In recent days, media reports had suggested the two sides were close to agreement.
The German weekly Der Spiegel reported on Saturday that German negotiators had presented Hamas with a new proposal, while the London-based daily al-Hayat reported that Khaled Meshaal, the Hamas political chief, was due in Cairo on Tuesday to approve a deal.
But by Sunday, both Hamas and the Israelis were playing down talk of a solution.
"Discussions about a deal [for Gilad Shalit] being secured in the next few days have no basis," Binyamin Netanyahu, the Israeli prime minister, reportedly told a closed cabinet meeting on Sunday, according to the Israeli paper Haaretz.
Shalit was captured in June 2006 in a raid by Palestinian fighters close to the border with the Hamas-run Gaza Strip.
He has become a popular cause in Israel and an embarrassment for successive governments, who activists accuse of not doing enough to secure his release.