The 18-year-old has made a strong start to the season this year, inspiring United to a comeback win against Sunderland earlier this month and has recently committed his future to the club by signing a new five-year contract.
With United trailing Stoke 2-1 at Old Trafford on Saturday, Januzaj came off the bench to inspire the Reds to a 3-2 win - and Van Persie believes the Belgian possesses all the attributes to be a ‘special’ player.
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"Over the years I've seen so many young players and I can honestly say that of all the young players I've seen he is right up there in the top one or two.
"He's a special player. He will give Manchester United a great bunch of goals and great games."
Januzaj’s potential has drawn comparisons with Van Persie himself, but the Dutch all-time top goalscorer insists the Belgian is unique in his own right rather than the new ‘Van Persie’.
He added: “He’s confident in a good way. He’s not too bothered with the whole occasion or the pressure of the games.
"When I go back 10 years when I was quite young I see similar attributes.
"I was very confident as well and I see some stuff in him and the choices he makes that I made when I was younger as well.
"He's a very big talent and he will be looked after by the staff and players here.
Januzaj is expected to start Tuesday night when Manchester United host Norwich City in the fourth round of the Capital One Cup.