The York Street base in the city centre has served as the home of the publications for decades and the first Sheffield Daily Telegraph was published on the site in 1855.
Johnston Press, which publishes both The Star and Telegraph, is looking at other office space available in the city.
A company spokesperson said: “York Street is one of Johnston Press’ largest properties, housing around 400 of our team members.
“We know that the office is not up to scratch and are currently looking at two options to ensure the team works in a comfortable environment that is fit for purpose.
"One option is to completely refurbish the office, the other is to relocate to new accommodation within Sheffield.
“In order to ascertain the feasibility of moving to new premises, we need to establish how easy it would be to sell the York Street property, hence the current marketing activity.
“No firm decisions have been made yet, we are simply putting out the feelers at this stage.”
* Closing date for offers is Friday, March 17, at 3pm. Contact Rapleys on 0370 7776292.