TMN, which is headed by chief executive Mark Smith, owns email and website marketing agency TMN Media, full service digital advertising agency EDR, online fieldwork service arm ID Factor, and research analysis agency ICD Research.
for £9.8m in December and Dutch online direct marketing agency for up to £7.9m in January.
Tangent's potential offer is pitched around 50p per TMN share, payable in a mixture of cash and Tangent shares.
Tangent said it has received acceptances from two investors in which own around 11% of the company, on condition that TMN does not receive a higher offer from a third party.
Michael Green has a 32% stake in Tangent, which is run by his nephews Nick and Tim Green.