Infront, which had been widely expected to win the deal, has held the rights negotiating contract since 2009 and was bidding to have it extended until 2021.
Lega Serie A, the association of Italy's top league football clubs, has proposed offering Infront a three-year deal which would be automatically renewable for another three years, dependent on meeting certain pre-agreed targets.
"The assembly unanimously agreed to make an offer to Infront on the basis of which we will open negotiations," Beretta told reporters in Milan.
The League, which rejected a rival offer from international sports agency IMG, will now hammer out the final details with Infront before signing a final deal, which would run from the 2015-2016 season.
Infront had guaranteed a minimum of 900 million euros (£744.96 million) a year to the clubs for the next three seasons and another 930 million for the three seasons after that in a six-year deal worth 5.5 billion euros.
But the offer covering the second period may be revised during the course of negotiations which will be led by Juventus chairman Andrea Agnelli and Claudio Lotito, chairman of Lazio.
Infront's proposal had the backing of Mediaset, Italy's biggest television broadcaster, and a group of 13 clubs led by AC Milan. But it faced opposition from other clubs including Juventus and News Corp's Italian unit Sky Italia.
Sky Italia has long been unhappy with the status quo, which it says holds back development of the game and favours its rival, Mediaset, owned by Silvio Berlusconi, the former prime minister and boss of Serie A club AC Milan.
In its current form, the contract, unique in Europe, awards television rights on the basis of delivery platform - satellite or digital terrestrial - but charges widely different prices to the two main broadcasters.
Sky has held the rights to broadcast on satellite while Mediaset broadcasts via digital terrestrial. Sky has proposed creating packages of different matches for which broadcasters could bid to offer exclusively but Mediaset has indicated it prefers to maintain the current shared system.
($1 = 0.7394 euros)
(Reporting by Danilo Masoni, writing by James Mackenzie. Editing by Jane Merriman)
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