Benitez departed as manager at St. James’ Park at the end of his contract this summer and his successor is yet to be confirmed.
Arteta, who works as an assistant to Pep Guardiola at Manchester City, and Nice boss Vieira, were both on Toon owner Mike Ashley’s shortlist, reportsThe Sun.
However, the newspaper believes that Arteta ruled himself out of the running after a conversation with Benitez in which he was critical of the Newcastle hierarchy.
Vieira made the same decision last week after a similar chat on the phone with the Spaniard, who is now in charge of Chinese Super League side Dalian Yifang.
Sheffield Wednesday manager Steve Bruce has now emerged as favourite for the job despite only arriving at Hillsborough in February.
Newcastle are eager to appoint a new boss soon, with a pre-season trip to China looming on Saturday, and the 58-year-old is understood to be keen on managing his boyhood club.