The Guardian claims that the Irons are "seriously" considering paying the £6million it would take in the Spaniard's contract at St James' Park to trigger his release clause.
Ashley has said that he wants Benitez to stay, but the pair have not held face-to-face talks and there is a lack of trust on Benitez's side after three botched transfer windows. Two league titles, two cups, one Super Cup and a brilliant Champions League campaign.
"The club expect to make an announcement within the next seven days, following a thorough and strategic process that has identified the best possible candidates".
Joint chairman David Sullivan said: 'This is an exciting time for our football club.
Benitez wants to be given assurances about exactly what he will have to spend on new players this summer before putting pen to paper and a lack of clarity concerning that means a new contract being signed isn't close to happening.
'Everything is in place to move forward. Hopefully Mike can preserve his phrase and we are able to do what we need to do.More news: N.Korea Will Be Rich, Protected If It Forgoes Nukes
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"I feel Gazidis will go for it", he added.
He mentioned: 'After I had the assembly with Mike Ashley (in Might, 2017) I used to be assured that we now have the cash obtainable and the wages.
'Then the assembly was essential to persuade me to remain.
Gooners, would you like to see Rafa Benitez take charge?
Ashley has again pledged to give Benitez "every last penny the club generates" after he guided them to a 10th-placed finish, with the owner insisting he would reject any approach for the manager.
However, the former Liverpool and Chelsea manager is growing increasingly exasperated.