The two experienced managers had a simmering feud following Mourinho's arrival in England in 2004, fuelled by a number of high-profile encounters between the teams, including a Champions League semi-final tie in 2005 that was decided by a controversial Luis Garcia goal.
The animosity reared its head again in 2015 when Benitez's wife commented on her husband's role in "tidying up the messes" of Mourinho, the Spaniard having taken charge at Inter, Chelsea and Real Madrid after Mourinho's spells at those clubs.
However, speaking on Friday, the United boss made it clear he has huge admiration for Benitez's successes, telling a news conference: "I respect him as both a person and as a professional.
"He is with me in one privilege on the list of the few managers in Europe that won the Champions League and the Europa League, so we are side to side in that little group and I have immense respect for him. So, I am more than happy to see him and to salute him, and then to play one more match because at the end of the day, it's just one more match.
"I know the way Newcastle play, I know the way Benitez prepares his team, I know that it's going to be difficult but we have to try to get back to the points that we need."
Mourinho had earlier confirmed Zlatan Ibrahimovic, Paul Pogba and Marcos Rojo will all be in the squad for the visit of Newcastle.
Pogba has been unavailable since suffering a hamstring injury in September, while Rojo and veteran striker Ibrahimovic are both yet to play this season, having sustained serious knee injuries in April.
The former Sweden captain suggested this week he will shift to a number 10 role this term behind Romelu Lukaku, and Mourinho admits he hopes to be able to fit both into this set-up.
"They are good players, they can play together," he said. "The problem is when the players aren't good, but with good players, it's easy [for them] to play together."
"For Romelu to be so young, beating the record, is fantastic," he said. "Romelu is very young and I think he has 10 more years to play for his country, so I can imagine [his total] number of goals [for Belgium] will be amazing."