A week before the deadline to enter the June 10 presidential election, feelers were still being put out Tuesday to and from potential new candidates.Sources close to former Foreign Minister David Levy said he had received overtures from Likud activists and MKs to join the crowded field. Levy is respected by Yisrael Beytenu chairman Avigdor Liberman, who made Levy’s daughter, Orly Levy-Abecasis, an MK.But Levy’s associates declined to say whether he was interested in being president.They said Levy has been pushed to run for months and that nothing had changed.Tel Aviv Chief Rabbi Yisrael Meir Lau’s office denied a report that he was actively seeking the presidency. Army Radio reported that he was trying to use his close ties to Prime Minister Binyamin Netanyahu to become a candidate.Netanyahu will meet with Negev and Galilee Development Minister Silvan Shalom for the third time in under a week on Wednesday to try to reach an agreement on the prime minister endorsing him. Shalom could sit the race out if Netanyahu does not back him.If Shalom and other potential Likud candidates do not enter the race, it would be a boost for the party’s only MK who is definitely running, former Knesset Speaker Reuven Rivlin. He vowed to keep the presidency apolitical if elected in an article published on Tuesday on the Israel Democracy Institute website.“On the constitutional level, the president is more a symbol than a center of authority,” Rivlin wrote. “Only when the president observes strict political neutrality and adheres to the ideal of nonpartisanship for which he was elected can his statements and actions have influence.” Rivlin singled out the president’s right to determine which party leader forms a government as an example of how the institution’s power is limited. He said Israel’s political history had proven that it is elections that really determine who the president entrusts with forming a government and that very rarely has a president had to make a choice.Knesset Speaker Yuli Edelstein complained about how dirty the race had become in an Army Radio interview on Tuesday morning. He said that if the campaign continued in such fashion, there will be an outcry to eliminate the presidency far in advance of the next presidential race seven years from now.Four candidates have been the subject of investigations – in the police or the media – since the campaign began.Former judge Dalia Dorner said she does not believe she will be targeted by any probes.“The only thing they can find on me is that when my children were young, I came home too late, but they turned out okay,” she told Israel Radio.