The 20-year-old striker has been linked with a host of Championship clubs after scoring 20 goals in 38 games for the Robins last season, helping them reach the League One play-off final.
Last week Fitton rubbished reports Cardiff had made a move for Austin while Burnley were then mentioned in the national press.
Nottingham Forest and Middlesbrough are thought to be leading the race for Austin and Fitton has warned they will have to dig deep to tempt Swindon to sell the youngster, who joined from non-league Poole in October.
"I would not get out of bed for £1million," he told the Swindon Advertiser.
"They would be dreaming if they thought he could be brought in for that sort of money.
"He's not for sale and it would take a very special offer from a very special club to prise him out of our hands.
"I think there's a lot of people who would like him and would try to unsettle him, but we're very firm on where his future lies."