Tangent's offer to buy the company for £40m was spurned by TMN directors on the grounds that it substantially undervalued it. However, it has opened the way for other suitors, understood to include venture capitalists 3i and August Equity, as well as Trinity Mirror.
TMN Group companies include full service digital advertising agency EDR, online fieldwork service arm ID Factor, and research analysis agency ICD Research.
TMN, which is run by Mark Smith, said: "It remains in discussions with several parties in relation to a potential offer for the company. These discussions, while progressing satisfactorily, remain at an early stage and there can be no certainty that an offer will be made for the company."
Interest in the company pushed TMN's share price as high as 57.5p last month, with reports that directors are unlikely to accept an offer below 60p a share.