Sony Music V-P communications Gary Farrow, a long-time friend of Outside founder and CEO Alan Edwards, has also been involved in discussions.
It is believed one option discussed is for Incepta, whose portfolio of PR firms includes The Red Consultancy, to take a majority stake in Outside, with Farrow becoming a part-owner of the agency.
Outside insisted a deal had not been struck, saying: 'Specific talks with Incepta are speculation.'
An Incepta spokesman declined to comment while Farrow himself, denying reports last week that he had left Sony, said: 'Nothing is happening.'
While Farrow has known Edwards for more than two decades, there are close links between Sony and Outside.
Jonathan Morrish, corporate PR head at Outside, quit Sony to join the agency in 2003 and continues to handle its corporate PR.
Sony referred calls about Farrow to Outside.
One Incepta source told PRWeek: '(The deal) was mooted but it's gone very quiet.'