Manchester City are reported to be heavily interested in the Dutch forward, who has only one year left on his Gunners contract.
However, the Emirates Stadium chairman has revealed that there has been no offers tabled for the Premier League's top goalscorer, nor would the club be interested in entertaining any bids.
“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,” Hill-Wood told reporters.
“We're not in the remotest bit interested in selling him.”
Reports suggest the 28-year-old Van Persie, who endured a disappointing Euro 2012 with Netherlands, is stalling on a £130,000-per-week deal.
Real Madrid and Barcelona have also been linked with the Arsenal man, but City are reportedly leading the queue for his signature, having already made contact with agent Kees Vos.
Manager Arsene Wenger also seemed to rule Van Persie out of a possible move to Juventus after denouncing the "low-level" nature of Italian football in comparison to the Premier League.
Hill-Wood's previous admission that Arsenal wouldn't break the bank to keep Van Persie in north London appeared to fuel yet more speculation, but the English champions' are also pursuing a similar stance.