Cisse has failed to make the expected impact at Lazio since joining the Italian side from Greek side Panathinaikos over the summer.
“Djibril is one of the players we admire at Auxerre, which is where he was formed, and we know his qualities as a striker,” said Bourgoin.
“We’re struggling for goals and we’re thinking about this solution. We’ve looked at other great players apart from him, in France and abroad, who have scored lots of goals, are internationals, but who are having trouble at their clubs.
“Recently, Djibril admitted that he dreamed of getting back into the France squad and returning to the French league with Marseille or Auxerre, where he’s already played. And if he had to choose, it’d probably be Auxerre.
“He’s held out a branch – not a telegraph pole, but it’s clear that we’ve responded to it.
“Nothing’s been done for the time being. Lazio are not loaning or selling.”