Yarm School could quit the town if its plans to move to the outskirts are rejected.
The D&S Times learned this week that neighbouring authorities were keen to tempt the independent school elsewhere
It hopes to move to land in Green Lane but planning permission is not guaranteed.
The site is classed as a green wedge by Stockton Council and conservation groups oppose development on open land.
On Tuesday, Yarm Town Council heard the school could move into North Yorkshire.
Members had not intended to discuss the move this week, but the issue was raised by Green Lane resident, Peter Roy.
Chairman Coun Liz Marsden said: "We've been told other councils would like to have Yarm School in their area - perhaps ten or 15 miles down the road."
Coun Marjorie Simpson added: "North Yorkshire County Council would love to have it. But it would be mistake if we were to lose Yarm School. It would be very bad for the town."
On Wednesday, head teacher David Dunn told the D&S Times that approaches had been made.
"There are many advantages in having one of England's leading independent schools in your area, with all it offers in employment and facilities," he said. "Yes, we have looked around at where this school should be located, However, our current preference is for Green Lane and that's the site we're presently working on.
"We're looking at all options, carrying out feasibility studies, and looking at traffic patterns around Green Lane at different times."
He said most pupils lived in the Yarm area, but many others travelled from further afield, including North Yorkshire. The school's location was important to where families bought homes, he said.
"I've spoken to four families this week who are considering taking jobs on Teesside, depending on Yarm School. The school has a considerable pull on people who are considering re-locating to the area."
Yarm Town Council is keen to see a swimming pool built somewhere in the town and Mr Dunn said: "We've offered to talk about shared facilities, a number of which could be of interest to the community."
Mr Roy told the town council that if the school moved, it would alter the town's character drastically.
"The old sites will be developed but what will happen to playing fields at Aisalby and Green Lane?" he asked. "I'm very concerned, partly because this proposed Green Lane development is six-feet from my front door, but also because Yarm could become a massive housing estate."
He criticised a Green Lane traffic survey carried out during half-term when school traffic was absent.
He also feared pupil numbers would expand greatly.
Yarm Town Council agreed to seek an informal meeting with Mr Dunn.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article