Liverpool and Chelsea are monitoring the situation with the England international in case the Gunners can't keep him at the club. Sources also suggest that Italian giants Juventus are also planning a shock move for the 23-year-old.
Walcott, who is out of contract at the end of the season, has rejected Arsenal's offer of £75k weekly. The Gunner is eyeing an improved deal worth £100,000-a-week.
Meanwhile, manager Arsene Wenger remains confident of Walcott's stay and said, "I think so. But I cannot tell you what he tells me."
"We are always in touch. He has character. He keeps focused and he wants to show he is 100 per cent professional and I have a big respect for that attitude," he said.
But chairman Hill-Wood insists the club will not spend more to keep the winger.
"We have got our general overall wage structure and we are not prepared to break it for anybody," The Daily Star quoted Hill-Wood, as saying.
"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," he added.
Walcott has started just 1 in six Premier League games, making five substitute appearances. The former Southampton star has lost his place after the signing of winger Lukas Podolski while Gervinho has been in sublime form so far, netting three goals for the season.
Arsenal are already eyeing Walcott's replacement in Crystal Palace's forward Wilfried Zaha.
The Gunner has scored twice this season, one against former club Southampton and the other was a crucial second half goal against West ham at the weekend.