The 28-year-old striker finished as top scorer in the Premier League last season and confirmed his intention to part ways with the Gunners earlier in July, which has started a transfer pursuit between Manchester City, Manchester United and Juventus.
However, the Emirates Stadium chairman insisted that Van Persie will not be sold on the cheap.
“He is a world-class player and we don’t want to give him away,” Hill-Wood told the Daily Star.
“If he is determined to leave that is up to him, but giving him away is not on our agenda.
|8/1||Robin van Persie is 8/1 to be the top Premier League goalscorer in 2012-13 with Paddy Power|
“To be honest I do not understand him at all. I understood Cesc Fabregas wanting to go home to Barcelona last summer. I had sympathy with that.
“But I thought Robin was happy at Arsenal, especially after the season he had with us.”
Van Persie has been part of the Gunners' squad since 2004 and was given the captain’s armband on a permanent basis after Fabregas left last summer.
Lukas Podolski and Olivier Giroud have already been brought in to the club recently, while Santi Cazorla is a reported £16 million target for the Gunners.