Chief executive Andy Penn on Monday proposed about 8300 staff who regularly come into contact with customers and colleagues be vaccinated as a condition of employment.

"More than most other companies our teams stretch across the far reaches of Australia - from our cities to remote outback towns," Mr Penn said in a staff email.

"We are part of these communities and we have an obligation to keep them safe and well - as to protect each other."

Telstra is proposing workers in people-facing roles have their first jab by October 15 and second by November 15. This does not apply to those working from home.

Mr Penn said exceptions would only be considered on medical grounds.

Workers would need to provide medical evidence and have it assessed by a medical practitioner.

The company would try to find a new role for workers whose claims were justified. If another role could not be found, the worker may have to leave.

Telstra officials will discuss the proposed policy for one week with staff, unions and customers.

A spokeswoman for the Communications Electrical Plumbing Union said Mr Penn should be wary of sacking workers who may have a genuine medical exemption to vaccination.

"The law doesn't provide for this, public health measures do not provide for this and we will be challenging this quite strongly," she said.

The union supports vaccination and has been lobbying employers for vaccination leave and incentives to get the jab.

The Electrical Trades Union has also been contacted for comment.

Mr Penn said the timing of the proposal was due to increased supply of vaccine and the spread of the Delta variant.

Big businesses are taking different approaches to vaccination.

Canned food producer SPC last month became the first Australian employer outside health care to require staff be vaccinated for the coronavirus.

Woolworths boss Brad Banducci last month baulked at requiring staff be vaccinated. He said the company was making vaccination easier by providing on-site clinics for staff.

Australian Associated Press