According to Al-Madina, quoting sources, the German mediator told Hamas that Barghouthi would be freed but other prisoners on the Islamist movement's list would not.
Barghouthi's wife Fadwa told a German anti-nuclear war delegation visiting Ramallah that she too had also received word that her husband would be released in the prisoner swap deal.
The Fatah leader, convicted in 2004, has been on the list of nearly 1,000 prisoners Hamas hopes to release in exchange for Shalit but the Israeli government has previously refused to concede. Many on the list are high-ranking Palestinian factional leaders.
Shalit was captured in a cross-border raid in 2006. Previous talks collapsed when Israel refused Hamas' demand that it released prisoners "with blood on their hands."
In early October, an Israeli minister said his government should consider the release of such prisoners if it would secure Shalit's return.
The report follows confirmation on Sunday by the Israeli government that talks on the prisoner swap deal have resumed after months of stalemate.
However, the soldier's grandfather Zvi Shalit told the Army Radio that Netanyahu's claims were false, and that the premier was killing Gilad by failing to secure his freedom, Israeli daily Haaretz reported.
On the same day, Hamas spokesman Ayman Taha said that the German mediator had visited Gaza to discuss a prisoner swap deal, but said no progress had been made on the issue.
The visit did not signify a resumption of talks on the deal, Taha said, describing the mediator's visit as "exploratory," in an interview with Ma'an Radio. The mediator brought no new information, he said at the time.