But Ratcliffe would like him to take over at Newcastle.
Premier League champions Manchester City have warned the Magpies off making a move for Mikel Arteta who was in the running to take over at Arsenal last summer.
Newcastle announced the departure of Benitez earlier this week in a move which angered fans.
A statement from the club read: “It is with disappointment that we announce manager Rafael Benitez will leave Newcastle United upon the expiry of his contract on 30th June 2019.
Newcastle dealt blow in pursuit of Patrick Vieira as Rafa Benitez replacement - EXCLUSIVE (Image: GETTY)
“We have worked hard to extend Rafa’s contract over a significant period of time, however it has not been - and will not be - possible to reach an agreement with Rafa and his representatives.
“Rafa’s coaching staff, Paco de Miguel Moreno, Antonio Gomez Pérez and Mikel Antia, will also leave the club on 30th June.
“We would like to thank Rafa and his coaching team for their efforts over the last three years and their significant contribution to what has been collectively achieved.
“We would also like to thank our supporters, players and staff for their patience during a period of uncertainty.
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Newcastle dealt blow in pursuit of Patrick Vieira as Rafa Benitez replacement - EXCLUSIVE (Image: GETTY)
“The process to appoint a successor will now begin.”
Rangers boss Steven Gerrard has also been linked with the Newcastle job.
The Liverpool hero has insisted he is happy at Ibrox though.
Rangers pushed Celtic into their first title race in years, and Gerrard wants to continue his project before moving on.