Dutch media site VI.nl, as quoted by talkSPORT, is reporting that AS Roma are leading the race to sign the 19-year-old Netherlands international.
The same article states that Kluivert could be heading to the Italian capital despite a host of Premier League clubs chasing the winger’s signature.
Arsenal, Chelsea, Manchester United and Tottenham Hotspur have all been linked with the Dutch talent ahead of the 2018 summer transfer window.
According to the same story, the Ajax winger has little over 12 months remaining on his current deal to open up the possibility of a summer move.
Kluivert has scored 10 goals in 30 games in the Eredivise this season to help the club finish behind PSV Eindhoven in the title race.
Manchester United were 2-0 winners against Kluivert and his Ajax team-mates in the Europa League final in Stockholm last season.
The Red Devils will be looking to add more pace to their team this season given Anthony Martial and Marcus Rashford are both facing uncertain futures at Old Trafford.
Chelsea FC are set to improve their squad in the summer following a disappointing defence of their title.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news