A number of manager have been linked with the job with the club's shortlist said to consist of Patrick Viera, Mikel Arteta and Rangers boss Steven Gerrard.
The Liverpool legend is in the Algarve preparing his side for the upcoming Europa League qualifiers.
Having been heavily linked with the Derby County job, which Rams owner Mel Morris labelled "absolute rubbish", Rangers won't welcome an approach from the mid-table Premier League side.
A club statement said of the reported Derby interest: “Our manager has not been approached and he remains 100 per cent committed to the job that he has here."
However, there will be no movement on the Newcastle job front until at least 4 July, according to the Scotsman's sister title The Shields Gazette.
The Magpies won't make approaches to possible candidates until after Benitez's contract expires on 30 June.
It has been confirmed that the club's U23 coach Neil Redfearn will take the club's pre-season training when they return on Thursday.