According to the Hebrew online news site Yedioth Aharonoth, the two vessels will wave banners describing "barbaric Hamas" and the Armenian genocide, allegedly in response to Turkish involvement in the nine-boat convoy.
"The [Israeli] fleet will go to confuse those who are coming to confuse Israel," the daily wrote.
The two fleets will not encounter one another as Israel's navy is set to declare the area south of Ashdod a closed military zone to prevent the Freedom Fleet from weighing anchor.
The MV Rachel Corrie, which raised anchor on Saturday, headed to the Mediterranean port of Cyprus, where it will join the Rachel, three Turkish ships and five from Greece all heading toward the Gaza port.
All nine boats are set to cast anchor at Gaza City's docks on 27 May, Palestinian lawmaker Jamal Al-Khudari said, following their rendezvous in Cyprus on 25 May.
The flotilla, organized by a coalition of groups from around the globe, will bring some 10,000 tons of reconstruction material, medical equipment and school supplies to the coastal region under siege.
Hundreds of activists protesting Israel's siege on Gaza will also be aboard the vessels, which will reportedly face a bevy of Israeli naval ships enforcing the Gaza blockade, though UN official in Gaza John Ging told a Norwegian paper that he saw no reason that a flotilla will be opposed.