Di Montezemolo says the "gossip" could be harmful to the Italian firm, which is continuing with efforts to cut losses and return to profitability.
His comments came at the same time as Fiat staff announced plans for a strike in December over job-cut fears.
"We're not going to create problems where there aren't any," Di Montezemolo says. "Everything else is just gossip that risks becoming harmful."
The Italian media has speculated that Fiat is keen to forge new partnerships with PSA Peugeot Citroen and Japan's Honda.
At present it shares some components with GM, such as the next generation Fiat Punto being based on the same platform as GM's Vauxhall and Opel Corsa.
Next month’s strike comes despite Fiat's pledge that its continuing cost-cutting efforts will not involve closing any factories or job cuts.
Back in July, Fiat posted losses of €282m (£198m), partly due to a strike, but also poor sales in Italy and across Europe.