US President Barack Obama is wavering about the potential nomination of former Republican senator Chuck Hagel for the position of defense secretary, according to a report published Sunday by the National Journal, a well-connected inside-the-Beltway publication.

Citing an anonymous senior administration official, the National Journal reported that Obama was now considering Michele Flournoy and Deputy Defense Secretary Ashton Carter for the position.

Should Obama pick Flournoy, who served as undersecretary of defense for policy before stepping down in the summer, it would be the first time a woman would be nominated to be Pentagon chief.

Hagel’s possible nomination has raised the objections of some American Jewish leaders who point out that the former Nebraska Republican senator, who left the Senate in 2008, had a problematic voting record on issues key to Israel – voting several times against US sanctions on Iran – and made disparaging remarks about the influence of what he called a “Jewish lobby” in Washington.

These comments were made to former US diplomat Aaron David Miller for his 2008 book, The Much Too Promised Land, in which Hagel was quoted as saying, “The Jewish lobby intimidates a lot of people up here.”

In 2001, Hagel was one of two senators who voted against renewing the Iran-Libya sanctions act, in 2007 he voted against placing the Iran Revolutionary Guards Corps on America’s list of terrorist organizations and in 2008 he voted against Iran sanctions.

Other problematic positions regarding Israel taken by Hagel include being one of only four senators in October 2000 who would not sign a letter of support for Israel during the second intifada, being only one of 12 senators in 2006 who refused to sign a letter calling on the EU to place Hezbollah on its terrorist lists and signing a 2009 letter – after he retired from the Senate – urging Obama to negotiate with Hamas.

But Hagel is not only under fire from Jewish or pro-Israel organizations, and on Friday he issued an apology for comments about gays he made during the 1998 approval process of a gay philanthropist, James Hormel, as the US ambassador to Luxembourg.

Hagel said in an interview at the time with an Omaha newspaper that Hormel was “openly, aggressively gay,” and that it would be an “inhibiting factor” for a US ambassador to be gay.

The Journal article quoted a senior administration official as saying it was “fair” to say Obama was considering other candidates.

South Carolina Republican Sen. Lindsey Graham said Sunday that Hagel’s nomination process would be challenging and that he would probably not get many Republican votes, and on Friday Texas Republican John Cornyn told The Washington Post that he would vote against the nomination.

Flournoy, whose name is now being bandied as a leading contender for the position, is a well-known figure in Israeli security circles, having served as the number three official in the Pentagon.

She spoke in May at the annual conference of the Institute for National Security Studies (INSS) in Tel Aviv and, addressing the Iranian nuclear issue, said Israel’s question of whether to go alone in attacking Iran or rely on a broader international effort sustained over time “comes down to your comfort level, your degree of strategic trust that the US will be with you, that others will be with you.”

Flournoy said Israel and the US’s strategic interests on Iran were fully aligned. Both realize a nuclear Iran will lead to a “cascade of proliferation in the Middle East” and both realize it will provide “greater cover for Iran” in the region and for its “destabilizing activities and support for terrorism.”

She said it all came down to the credibility of the US commitment.

“Do you believe that we see this in the same way and that the US will ultimately back up our statements with actions,” she asked.

She then quoted her mother and said “actions speak louder than words,” before listing a series of diplomatic actions she said the Obama administration has taken to back Israel.

During that speech she also addressed the tense Israeli-Turkish relationship, and advised Israel to act “more strategically” and reconcile with Ankara.

Flournoy, who played a key role in shaping Obama’s national security policy, characterized Turkey as one of the strongest and most influential voices in the region, remained a close and valued NATO ally for the US and shared “our interest in preventing Iran from becoming a nuclear weapon state.”

While acknowledging that she understood that “past events have made concrete steps toward reconciliation quite difficult,” she said that “if there is ever a time for Israel to rise above past differences and recriminations with Turkey, now is that time.”

Reuters contributed to this report.