Shropshire Council leader Peter Nutting said the authority is working with the school with a view to finding a new site for the future.
Several sites have been suggested, including Shrewsbury Sports Village in Sundorne, but Councillor Nutting said it is still very early days.
"We are looking at a potential new school in the Harlescott area for secondary children," he said. "It would be quite a big school with probably close to 1,200 students.
"Currently we are look at a number of sites. Among the sites suggested is the sports village but it is early days and we have hardly done any work yet because ultimately it is up to the academy. But Shropshire Council has said it will help them."
Councillor Kevin Pardy, local member for the area, revealed that the council is looking at Sundorne Sports Village as a possibility.
In a social media post, he asked local residents for their opinion.
But Councillor Nutting stressed that no decision has yet been made.
He added: "There is a lot going on at the academy at the moment so it is too early to say what will happen in the future but we are considering a number of options.
"There is obviously still the two Shrewsbury Academy sites to consider too, and there maybe other opportunities of land that could be developed.
"When things progress and we have something more concrete, of course we will start talking to the public, but at the moment we don't want to frighten anyone.
"This is far from a done deal and don't want anyone to think otherwise."
Earlier this year the school was rated 'inadequate' and placed in special measures by Ofsted. Inspectors visited Shrewsbury Academy in May and found that it failed in every area.
In June it was announced that it has been agreed in principle for Shrewsbury Academy to join the Marches Academy Trust before the start of the new school year.