Van Persie only has 12 months remaining on his contract at The Emirates 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, 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.
"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.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.