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 former Feyenoord attacker, 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.”
The Daily Mail are reporting that the 28-year-old Van Persie, who endured a disappointing Euro 2012 with Netherlands, is stalling on a £130,000-per-week deal.
The newspaper also claims that Juventus have had an £8 million offer rejected and plan to bid as high as £12m for last season’s Premier League top scorer.
Real Madrid and Barcelona have also been linked with the Arsenal man and Arsene Wenger will doubtlessly be desperate to secure the long-term future of his star player.