Although unconfirmed Constantine is reported to be joining Ellis Watson, the former Currantbun.com and News Group Newspapers marketing director, in launching a new internet content service.
Constantine joined News International in 1992 as a marketing manager for News Group Newspapers. He then moved to be marketing manager for Times Newspapers and was made marketing director four years ago.
Camilla Rhodes, managing director of Times Newspapers, said: "Toby has made a tremendous contribution over the past few years to the growing success of The Times and the market pre-eminence of the Sunday Times."