The team from Deeley Construction were immediately withdrawn from the halls of residence refurbishment job last week and the site has been shut ever since.
One worker told the Coventry Telegraph that their work clothes had been incinerated as a precaution.
The worker, who did not wish to be named, said: “I am worried – you don’t know what the long-term effects will be. We’re all going to be sent letters to notify our doctors that we’ve been exposed to asbestos.
“We all know it’s a killer, and you don’t know if it will start to affect you in 30 years’ time.”
A spokesman for Deeley Construction said: “We were aware there was asbestos in some parts of the buildings.
“We had hired a removal firm to move furniture. It subsequently transpired that some of that furniture was fixed to walls which contained asbestos and once that was reported to us, work was stopped on that building and the site closed.
“Testing is now being carried out and the facts will be reported to the Health and Safety Executive well within the permitted time frame.
“Deeley is a renowned and responsible construction company that has safety at the forefront of all its operations.
“We have fully communicated the situation with the university and we are working together to remedy the situation.”