Van Persie only has 12 months remaining on his contract and Hill-Wood admits they are not currently in talks with the Dutchman as he is taking a break following Euro 2012.
He has been linked with a move away from Emirates Stadium this summer, with Manchester City understood to be interested in securing his services.
Juventus, Real Madrid and Barcelona are also believed to be keen on Van Persie, who enjoyed a stunning campaign last season.
However, Gunners boss Arsene Wenger has always insisted that he expects to keep hold of the 28-year-old and Hill-Wood maintains they do not want him to leave after talk of a bid from Juventus emerged on Monday.
"As far as I am aware nobody has made any offer for him and he is away so we are not in any dialogue at all," said Hill-Wood.
"We're not in the remotest bit interested in selling him."
Reports suggest that Van Persie will speak to Wenger by phone this week in an attempt to sort out his future.
Arsenal have already strengthened their attacking options this summer with the signings of Olivier Giroud and Lukas Podolski.