The Dutchman has refused to comment on his future or discuss extending his current deal that is due to run out in 2013, insisting he will not do so until the end of the season.
And the chairman stated that while no talks have taken place with the striker himself, he has discussed the matter with manager Arsene Wenger, and they are optimistic that the 28-year-old will extend his stay in north London.
"We haven’t talked to Robin yet, but I spoke to Arsene (Wenger) recently. He is very confident he will stay and I very much hope he will, he has had a wonderful season with us," Hill-Wood told the Daily Star.
|4/7||Robin van Persie is 4/7 with bet365 to score at any time when Arsenal play West Brom on Sunday.|
Arsenal's game on Sunday against West Brom could go a long way to influencing Van Persie to stay, with a win guaranteeing Champions League football next season.Wenger is remaining calm about the subject, and is confident that his side will remain focused on coming away with a positive result.
"We have a massive game in front of us, but I feel we are focused, switched on. I am confident we will do well," the Frenchman told reporters.
"For us it is just to find the right mixture - to be focused, combative and relaxed, and especially be faithful to play our football like we want to.
"At the end of the day it will be down to playing well, no matter what is at stake."
Another factor in Van Persie's decision will be new signings. The Dutchman has often expressed his desire for the Gunners to improve their squad, and they've already added to the team with the signing of Lukas Podolski.
Wenger, however, insisted that no deal is in place for French international Yann M'Vila.
"It is not true. There is not any interest at the moment," said Wenger.
"We have not been in touch with anybody, we have not made any offer to anybody and we are nowhere near to buying anybody at the moment.
"We are focused on our final game of the season."