Benitez will officially leave Newcastle when his contract expires on June 30 and the Telegraph report that four names make up the shortlist to replace him: Patrick Vieira, Steven Gerrard, Mikel Arteta and Eddie Howe.
It is understood that the club would like a younger manager to succeed 59-year-old Benitez, though all four targets are thought to be happy in their employment elsewhere so may need convincing to move north-east.
Arteta has been linked with replacing Pep Guardiola when he eventually moves on from Manchester City and there are doubts as to whether Howe would leave the south coast.
Gerrard has made it clear that intends to stay at Rangers and build on a largely impressive first season in Scotland, while former Arsenal captain Vieira also enjoyed a solid first season with his club Nice, leading them to seventh in Ligue 1.
Newcastle have yet to make contact with those on their shortlist but they have spoken to Vieira before, prior to appointing Steve McClaren in 2015.
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