News International is hoping to sell its site in Wapping and is looking at property in Canary Wharf, the Guardian has reported.
Its current base houses the Sun, News of the World, the Times, Sunday Times and the London Paper and could be sold in its entirety or to individual buyers.
Clive Milner, the News International group managing director said there had been a high level of interest and "we think we will in the next month be able to say who the last three in terms of a sale are".
The group had delayed its move because of falling commercial property values and could share its next base with Dow Jones staff.
"These are possibilities but no decision has been taken about the shape of our new headquarters in terms of the shape of its components," Mr Milner said.
"Now we have got about three or four targeted buildings that we are still in detailed discussions with."