Falk & Co real estate agent Gary Attrill said the building started its life as the state bank before it was taken over as the Commonwealth Bank.

"It's a great block, central location, it's fantastic," Mr Attrill said.

He said it was the first time ever that the building, which was believed to have been built in the 1920s, had been put up for sale.

The laneway entrance to the large block at the back of the former bank building raised the prospect of the land being used for the construction of accommodation, similar to the block next door to it.

He said there had already been interest from buyers since the property was first listed late on Friday.

The site will go under the hammer on November 19 at noon.

It is expected to fetch between $2 million to $2.2 million.

The property features a commercial premises downstairs, and a four-bedroom accommodation facility upstairs.

The sale comes after the Commonwealth Bank decided to close its branch for good on July 30.

It follows the closure of the National Australia Bank in 2018 and the ANZ bank in August which just leaves the community Bendigo Bank in the seaside town.

The decision to close the Commonwealth Bank branch was made after a review showed face-to-face numbers using the facility had dropped 46 per cent drop over five years.

The building at 51 Sackville Street became the home of the State Savings Bank in 1926 before it changed to the Commonwealth Bank in 1991.

It was one of 14 branches across Melbourne and regional Victoria designed by a young firm of architects called Stephenson and Meldrum, which would go on to become one of the biggest in Australia.

All the banks included the traditional side entrance to the manager's residence upstairs.

Before moving to the Sackville Street site, the Savings Bank was located at 28 Bank Street on the north-east corner of Barclay Street which was built in about 1864.