Ruud Gullit has already warned that van Persie would struggle to get into the Arsenal team.
The former Chelsea and Newcastle manager, who takes over at Feyenoord in the summer, said: "I know how it works at a club like Arsenal and you can imagine that Robin will hardly play there in his first few years.
"I don't imagine that a player like Robert Pires will be on the bench in favour of Robin."
However, van Persie does not lack confidence in his ability and, like many Dutch footballers, is not afraid to express his opinions.
When he was put on the substitutes' bench last season following a spell out with a back injury, the youngster publicly criticised his coach Bert van Marwyk. A series of disputes followed and the player so infuriated van Marwyk that the Feyenoord boss banished him to the reserves.
Van Persie was eventually reinstated to the first team but then complained that he would rather play in a central striking role than on the left wing.
In October, chairman Jorien van den Herik claimed that the player's personal demands for a new contract were excessive and complained: "I hope that he returns to earth soon."
However, what is of little doubt is that van Persie has an excellent pedigree.
He was drafted into the Feyenoord first team at the age of 18 and played a starring role in the side which lifted the UEFA Cup in 2002. Despite the run-ins with van Marwyk last season, he still scored eight goals from midfield.
Van Marwyk said: "Robin is a fantastic talent and we would like to build a team around him. We have tried many times to get him to sign a new contract, but the boy refuses to sign."
A move for van Persie makes sense from Arsenal's point of view.
He can play as a support striker as well as on the left wing and may be considered a long-term partner for Henry.
Although Francis Jeffers is set to return to Arsenal next season, Bergkamp and Sylvain Wiltord are out of contract in the summer and Kanu's Highbury future is shrouded in doubt.
"For Robin it is a dream to continue his career abroad with a top team," said van Persie's adviser Erwin Boonacker.
"In December, Robin was visited by an Arsenal representative and we informed Feyenoord about the interest from London. When Feyenoord and Arsenal reach an agreement [about a fee], we will start negotiations with Arsenal."
