Reports have surfaced outlining proposals for redevelopment at the East of England Arena - but Chapman insists this will be a longer term project.
Chapman said: “We are in dialogue with the management at the Showground who have kept us in touch with developments.
“Whatever happens, it’s not an overnight situation. I fully expect the sport to continue at the venue for the next few seasons without actually putting a timescale on it.
“The Showground have been superb in keeping me updated and have been reassuring. There will be speedway there next year.”
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Chapman has described Thursday’s (September 5) narrow defeat by Belle Vue as a ‘brilliant meeting’.
He added: “I was gutted we lost because it was a great meeting.
“We had things which went against us but on another night we could have won it.
“Hans (Andersen) had a crash which I felt sick seeing it was that bad. He was back to his best, riding superbly and then crashed.
“I can tell you everyone in the Stadium was delighted when he walked away - it was a miracle!
“Congratulations to Belle Vue on the win but we could have won it. My thanks to the Peterborough fans for turning out to back us and we need them again on Monday.”
Swindon, who are chasing top spot in the Premiership, visit on Monday night (September 9) when Panthers will welcome back British Champion Charles Wright for his first appearance on home shale since taking the tItle.
And Scott Nicholls also returns from suspension but Jason Garrity will again miss out.