In a video circulating on social media, the 37-year-old Portuguese striker is captured limping off the pitch at Goodison Park before appearing to bend down and slap a mobile phone out of the hand of a young supporter.
A statement from Merseyside Police said they were in touch with both clubs after the game regarding “reports of an attack”.
“As the players left the pitch at 2.30pm, it was reported that a boy was attacked by one of the away teams as they left the pitch,” the statement said.
“Investigations are ongoing and officers are currently working with Everton Football Club to review CCTV footage and are conducting extensive witness interviews to determine if an offense has taken place.”
An update on the incident will be released shortly as more information is gathered, a Merseyside Police spokesman told CNN on Monday.
“It’s never easy to deal with emotions in difficult moments”
Ronaldo apologized for his “outburst” and in a message posted to Instagram on Saturday offered to take the fan to a game at Old Trafford, which put them seventh in the Premier League and six points behind Tottenham Hotspur in fourth leaves.
“It’s never easy to deal with emotions in difficult moments like the one we’re facing,” said Ronaldo.
“Nevertheless, we must always be respectful and patient and lead by example to all young players who love the beautiful game.
“I would like to apologize for my outrage and, if possible, I would like to invite this supporter to watch a game at Old Trafford as a show of fair play and sportsmanship.”
A spokesman for Everton told CNN the club are trying to contact the boy’s mother to invite the couple to the club’s next home game, a league game against Leicester City on April 20.
The invitation was “to reassure the boy that such incidents at football matches are not the norm and hopefully give him a positive reminder of visits to Goodison Park,” the spokesperson added.
Manchester United declined to comment on the incident, referring CNN to Ronaldo’s apology, which was posted on social media.