The Observer claims that in addition to the two publishers, its own parent company Guardian Media Group has discussed a joint bid, with private equity firm Apax, for some of Emap's radio assets.
Gruner & Jahr has no presence in the UK, but owns 90 magazines, one newspaper and 26 websites in most of Europe, Asia and Central and South America.
Lagardere is a conglomerate with business lines in book publishing, magazine publishing, French TV channels, magazine distribution and sports rights, and it also owns a stake in European aviation technology company EADS.
Its magazine division had a €1.8bn (£1.2bn) turnover in 2006. It expanded into the UK in 2002 by acquiring magazine company Attic Futura, and currently publishes titles including Elle, Red and Psychologies.
The two companies are likely to be interested particularly in Emap's consumer magazine portfolio and also its business-to-business publishing and events division, rather than its radio division.
Two weeks ago it emerged that Italian publishing group Mondadori, controlled by Silvio Berlusconi, had expressed interest in Emap.
The break-up of Emap is expected to fetch upwards of £2.5bn if all its three divisions are sold off.