Manquillo arrived in his native Spain on Thursday evening to undergo his medical ahead of finalising an 18-month deal to join La Liga side Celta Vigo.
The 29-year-old is due to see his Newcastle contract expire at the end of the season, but he plans to terminate his deal six months early in order to reunite with former Magpies boss Benitez at the Estadio de Balaidos.
Benitez signed Manquillo for Newcastle from Atletico Madrid in 2017 after the right-back had previously represented rivals Sunderland, Marseille and Liverpool all on loan.
Manquillo has featured in 110 games for Newcastle across all competitions, but he has not made a single appearance under manager Eddie Howe this season due to a series of troublesome muscle injuries.
The Spaniard has subsequently fallen down the pecking order at St James' Park, with Kieran Trippier, Valentino Livramento and Emil Krafth all preferred ahead of him at right-back.
Maquillo is hoping to reignite his career at Celta Vigo, and while a deal is close to completion, Benitez has insisted that "he is not our player yet."
Speaking about Manquillo at a press conference on Friday ahead of Celta Vigo's clash with Real Sociedad on Saturday, as quoted by The Shields Gazette, Benitez said: "There are last-minute paperwork issues. I imagine it will be resolved.
"What we are looking for is to improve the competitiveness of the squad in all the positions we can whenever we can. "[Manquillo] is a market opportunity, a player who has experience, who can help us in this stretch.
"If everything goes well, in many more games. I insist, he is not yet our footballer and comes to help, to add, to compete."
Asked if Manquillo could sign and be fit in time to make his debut against Sociedad on Saturday, Benitez said: "No.
"He is a player who is healthy once he finished a problem he had with his adductor, he ended up having surgery for an inguinal hernia to see if the problem came from there. He is fine, he has been training.
"Now it is a question of how long it will take for him to get fit. We are not bringing him for tomorrow. We are bringing him so that he is in shape as soon as possible and tightens so that those of us who are around can all get fit the batteries.
"If you are going to ask me if he is going to play tomorrow? No. First, because he is not our player yet, and second because he would not be fit."
Manquillo's expected departure from Newcastle comes at a time when the club are working with the constraints of Financial Fair Play and could be forced to sell a number of first-team players to balance their books.
Meanwhile, right-back Trippier is reportedly attracting interest from Bayern Munich, who have identified the 33-year-old as a potential target this month.