Ronaldo wants to quit United in a bid to play in the Champions League next season.
The 37-year-old has now asked the Premier League side to consider any reasonable offer, as he looks to continue his career at the highest level.
Bayern Munich and Chelsea have also been linked with Ronaldo.
But Napoli are now monitoring the situation, despite having Victor Osimhen in their ranks.
Osimhen himself is being eyed by clubs around Europe, having impressed last season for the Serie A side.
The Super Eagles star helped them to a third-place finish in the league after scoring 14 top-flight goals from 27 appearances.