The Portuguese star has encountered a difficult return to Old Trafford since rejoining the club from Juventus last summer.
Manchester United have had a woeful season that has seen them exit all cup competitions. The Red Devils are likely to finish outside the Premier League top four.
Arsenal fan Piers Morgan revealed he had urged the north London side to target the former Real Madrid man this summer.
But Parlour insists that Cristiano Ronaldo will not be joining Arsenal. He was asked whether the Gunners should sign him, to which he replied on talkSPORT (via HITC):
"Why not? If you could get him. But I don’t think he would want to go to Arsenal.”
Despite Manchester United's poor season, the veteran forward has continued his remarkable consistency. He has scored 22 goals in 36 appearances across all competitions.
He scored against the Gunners on April 23, although in vain. Arsenal would defeat United 3-1 all but ending the Red Devils and Ronaldo's hopes of a top-four finish.
Cristiano Ronaldo awaits Erik ten Hag at Manchester United with a move to Arsenal unlikely
Manchester United have announced the appointment of Erik ten Hag as their next permanent manager. The current Ajax head coach will replace interim manager Ralf Rangnick at the end of the season.
According to Fabrizio Romano, Ronaldo understands the situation at United and doesn't want to put any pressure on the club in such a difficult period.
He is therefore awaiting the arrival of Ten Hag to understand the project the Dutch coach wishes to implement.
He is likely to be joined by a striker who will ease the goalscoring burden on the Portuguese forward.
However, there is speculation that Manchester United's failure to qualify for the UEFA Champions League will see their star man exit.
One league that the legendary forward is yet to take hold of is the MLS. The States is where former Manchester United forward Garth Crooks believes the star should go.
"I am a huge admirer of Ronaldo. His professionalism is beyond reproach and he has more than fulfilled the expectations required of a 37-year-old player in the toughest league in the world. However, he is still a young man who needs a purpose in life."
"The United States might be the place to establish that purpose. David Beckham and Ronaldo would make a formidable partnership in Miami."
The veteran forward has a year left on his current deal at Old Trafford but speculation continues to grow over his future.