�As we didn�t accept the offer we won�t be releasing any details of it, as we consider them �commercial in confidence�,� chief executive Mat Humfrey said.
At last month�s meeting, councillors rejected the offer on the four lots comprising the car park at the west end of the street.
In July last year, councillors adopted a business plan for the sale of the car park, which is owned by the council, to help fund planned town centre improvements and a train station toilet.
At the time, staff reported any sale could reap �significantly� more than the $1.5 million needed to trigger a business plan.
However, mergers that could have prevented the money being spent in Cottesloe collapsed earlier this year.
Mr Humfrey said �several parties� had also approached the council �informally� about the council redeveloping some town centre sites.
Councillors subsequently agreed to contact all Station Street property owners about their support for redevelopment in the street and to discuss a better connection between the train station and shops with the Public Transport Authority.
Station Street landlord and developer Alan McGillivray has his office directly west of the car park but he said he did not make the offer or had heard �a wind or a whisper� of who made it.
�No, I haven�t shown any interest in it, mainly because of the zoning and use,� Mr McGillivray said.
Cr Rob Rowell said he would not support a sale because the land was bought by the council using money from developers and shopkeepers in lieu of their businesses not being able to have car bays.
�There are lots of places in Napoleon Street and other areas of the town that have no car parking, and they wouldn�t have any if they develop these lots on Station Street,� he said.
A Coles spokeswoman, and a spokesman for Woolworths, both said neither supermarket chain had made the offer.