The NBA is looking to set up a franchise league in Europe from 2027 for 16 teams based in some of the continent's major cities.
Franchises, though, would need to stump up at least $500 million, and potentially up to $1 billion, to take part, with the NBA promising to distribute hundreds of millions of dollars per year to the teams in return.
"The 13 shareholders unanimously rejected the offer, which they consider unacceptable in its current state," the source said, while adding that the EuroLeague teams had not closed the door on future negotiations.
Several media reports said that one of the participants at the meeting of EuroLeague clubs in Cernobbio in northern Italy had described the NBA offer as "colonialist".
The NBA's project envisages a new league comprised of 12 permanent franchises based in London, Manchester, Berlin, Munich, Madrid, Barcelona, Paris, Lyon, Milan, Rome, Athens and Istanbul.
The other four teams would be able to qualify for the NBA Europe competition.
The sums involved, though, raise questions as the major European basketball clubs are already losing money.
EuroLeague, which is the continent's primary competition, is itself due to grow from 13 teams to 21 for the 2027/28 season, with 15 teams having applied to be amongst the eight new permanent franchises admitted to the competition.
They would join Real Madrid, Barcelona, Vitoria, Olympiacos, Panathinaikos, Fenerbahce, Anadolu Efes, Bayern Munich, Asvel, Zalgiris Kaunas, CSKA Moscow, Maccabi Tel-Aviv and Olimpia Milano as shareholders.