The 37-year-old was interviewed by Merseyside Police in relation to an allegation of assault and criminal damage following the incident on April 9, when footage showed the Portugal international appearing to knock the supporter's mobile phone to the ground as Ronaldo limped towards the tunnel following United's 1-0 defeat.
While the police investigation concluded with the issuing of a caution, the PA news agency understands the FA will now reopen its case against Ronaldo and seek the player's observations.
A Merseyside Police statement said: "We can confirm that a 37-year-old man voluntarily attended and was interviewed under caution in relation to an allegation of assault and criminal damage.
"The allegation relates to an incident following the Everton v Manchester United football match at Goodison Park on Saturday April 9.
"The matter has been dealt with by way of conditional caution. The matter has now concluded."
After the incident, Ronaldo issued a social-media apology for his "outburst" and invited the supporter to watch a game at Old Trafford "as a sign of fair play and sportsmanship".
Taking to his Instagram account after the match, the Portuguese forward said: "It's never easy to deal with emotions in difficult moments such as the one we are facing.
"Nevertheless, we always have to be respectful, patient and set the example for all the youngsters who love the beautiful game.
"I would like to apologise for my outburst and, if possible, I would like to invite this supporter to watch a game at Old Trafford as a sign of fair-play and sportsmanship."
Manchester United and Ronaldo's representative have been contacted by PA for comment.