Opinion polls show that while Mofaz, who is a deputy prime minister, is highly ranked in the contest to lead the Kadima party, he trails Tzipi Livni, the foreign minister.
Olmert, who is currently under investigation for corruption, said last week he would step down once a successor for the party leadership has been chosen.
The party leadership election is to take place next month.
While he supports diplomacy to resolve the standoff with Tehran, Mofaz said in June that an Israeli attack to halt Iran's nuclear project may be "unavoidable" unless a deal was reached.
Iran says its nuclear development is for civilian purposes only, to produce energy.
Israel is widely believed to have assembled the Middle East's only nuclear arsenal which experts say comprises as many as 200 warheads.
Israel does not discuss its nuclear capabilities under a so-called "strategic ambiguity" policy.