By Nadia Damouni

NEW YORK, July 5 (Reuters) - The race to become Yahoo Inc's next chief executive appears to have come down to two candidates: current interim CEO Ross Levinsohn and Hulu CEO Jason Kilar.

According to two sources with knowledge of the situation, Levinsohn and Kilar are the last names left on the Yahoo board's shortlist for permanent CEO of the company.

Yahoo, the once iconic Internet company, has struggled to find its footing in the new digital world dominated by the likes of Apple, Google, Facebook, and Twitter.

The company has essentially been rudderless since turning down Microsoft's $44 billion takeover offer in 2008. Since that time, Yahoo has plowed through four CEOs in as many years, among them Terry Semel, co-founder Jerry Yang, Carol Bartz, and most recently, Scott Thompson.

Yahoo's board also had on its shortlist Jonathan Miller, currently News Corp's Chief Digital Officer and former CEO of AOL Inc, and wanted to speak with him about the position, but Miller declined to pursue discussions, said a source familiar with his thinking.

According to this source, Miller put the brakes on any talks with Yahoo's board out of respect for his friendship with Levinsohn, who has long wanted to run a company as CEO. Prior to their current positions, Miller and Levinsohn ran an investment firm together named Fuse Capital.

Kilar, however, has no such personal relationship with Levinsohn, which is why he is still on the shortlist.

Executive recruiting firm Spencer Stuart is leading the search on behalf of Yahoo.

While Kilar is being seriously considered for the role, Levinsohn is still thought of as the favorite to take the position on a permanent basis, according to one of the sources.

Since taking over as interim CEO in May after Scott Thompson's forced resignation, Levinsohn has been acting and making decisions as if he has already won the seat, this source said.

Levinsohn hired former Google director and media veteran Michael Barrett as Chief Revenue Officer to help lead Yahoo's efforts to reemerge as an entertainment and information destination that wins advertising revenue.

Those close to Levinsohn have said he is committed to building out Yahoo's own video programming and striking more syndication deals in pursuit of ads that command a higher price, and Barrett's hiring underscores that strategy.

Miller and Levinsohn were not immediately available for comment. A spokesman for Yahoo's board, Charles Sipkins, declined comment, as did a representative for Hulu.