SocGen shares were up 1.7 percent at the market close, giving SocGen a stock market value of roughly 40 billion euros ($59 billion) a week after France's second-largest bank disclosed 4.9 billion euros ($7.3 billion) of losses and blamed them on one trader, Jerome Kerviel.
In 1999, SocGen escaped a takeover bid by BNP Paribas. There has been consistent market speculation since then of a merger between the two.
GSD Gestion fund manager Jacques Gautier said a tie-up between BNP Paribas and SocGen would be good for shareholders in both banks. "Overall, it will be boost profits."
"In terms of the French retail banking network, it will double BNP's capacity. There would also be cost cuts as the two banks overlap in many areas," he said.
Meanwhile, France was heading for a clash with its European Union partners after Jean-Claude Juncker, chairman of the Eurogroup set of euro-zone ministers, said a bid by a foreign player would not be surprising.
"When we are in very sensitive sectors, and the financial sector is one, because it's structural for the economy, it's normal that the public powers look at how and whose hands the French money is in," said France's minister for European affairs, Jean-Pierre Jouyet.
"If someone coming from abroad wanted to do good things with SocGen ... why would that bother me?," Juncker, who is also the prime minister of Luxembourg, said on Europe 1 radio.
A senior adviser to President Nicolas Sarkozy also weighed in to warn off foreign predators.
"The state will not remain just a bystander and leave Societe Generale at the mercy of any predator," adviser Henri Guaino told BFM television. French Prime Minister Francois Fillon said earlier this week that "the government is determined that Societe Generale remains a great French bank."
Thursday's exchanges came a day after EU Internal Market Commissioner Charlie McCreevy warned France that competition rules would apply to the treatment of any bidders.
"In a situation of potential takeover, free movement of capital rules provide for undiscriminatory treatment of potential bidders," McCreevy said in a statement from his spokesman.
Analysts say foreign banks, including UniCredit, Santander, BBVA and HSBC, as well as BNP Paribas, are on a long list of potential bidders for the weakened bank.
SocGen has said it is strong enough to stay independent.
Morgan Stanley, one of two investment banks underwriting a planned capital increase to plug the hole caused by the rogue trades, meanwhile said it had cut its price target on the shares to 115 euros from 154.
Its analysts kept an "overweight" rating on the stock and a "positive view" on the company.
On Wednesday, SocGen's board resisted government pressure to sack its Chairman Daniel Bouton, voting unanimously to keep him in his job.
But Thursday's French newspapers said the appointment of a committee of independent directors to oversee an inquiry into the crisis meant he was "under surveillance".
According to an official of the CGT trade union, senior SocGen employees have called for a demonstration outside SocGen headquarters in the La Defense financial district for 3:30 p.m. (1430 GMT) on Thursday in support of Bouton and the bank's independence. He said the demo was not sanctioned by any unions.
Police on Wednesday raided the flat of Olivier Kerviel, brother of the 31-year-old trader and a former BNP Paribas trader, according to sources close to Olivier Kerviel.
It was not clear whether the raid was in connection with the SocGen scandal.