TMN has already received an approach from Tangent Communications and has also been contacted by other potential buyers, reported to be August Equity and 3i. According to the Sunday Times, Trinity Mirror has now expressed interest.
The interest has pushed up its share price, although this morning's price of 52.5p per share is down from the high of 57.5p it hit last month when TMN confirmed it had received other approaches.
At the same time, former Datamonitor boss Mike Danson has been building up his shareholding in the business, and now owns around 12% of its shares.
TMN rejected the £40m Tangent bid on the grounds that it significantly undervalues the company. It is thought that it is unlikely to accept an offer below 60p per share, compared with Tangent's offer of around 50p.
TMN companies include full service digital advertising agency EDR, online fieldwork service arm ID Factor, and research analysis agency ICD Research.
Last week, in a deal worth up to £5.8m.
A Trinity Mirror spokesman said the company would not comment on speculation.