Walcott is out of contract at the end of the season and the England winger has reportedly rejected Arsenal's latest offer of ?75,000-a-week wages as he looks for a better deal.
Talks are ongoing but as yet no new deal has been agreed, with Liverpool and Chelsea said to be interested in signing Walcott if he can't reach a compromise with the Gunners.
Arsenal manager Arsene Wenger remains confident Walcott will stay, but Hill-Wood insists they will not break the bank to please the former Southampton player.
"We have got our general overall wage structure and we are not prepared to break it for anybody," Hill-Wood told the Daily Star.
"We have made an offer which he didn't think was acceptable and that is the end of it. We think it is a very reasonable offer.
"For the moment his people are still talking to us and we hope it will be resolved. But don't ask me when, because I haven't a clue.
"I hope that he will eventually come round and sign. It will be a pity if he does not, but the whole issue of pay for footballers has got totally out of hand and they don't get terribly well advised a lot of the time."