“The country is more important than one person’s advancement, and the country now needs a unified right,” he added.
Ms Shaked said it was time for the Israeli right-wing beyond Likud to unite.
“A union is the ideological right wing’s insurance certificate,” she said, according to the newspaper.
“Together, under my leadership, we’ll become a significant and powerful force that will lead the State of Israel with courage and faith.”
Talks over a potential alliance between New Right and the United Right List, the latter of which includes Ms Shaked and Mr Bennett’s former party Jewish Home, have so far not generated results.
Benjamin Netanyahu dismissed the two New Right leaders from their ministerial positions last month, replacing them with Jewish Home MKs.