France forward Giroud has made only two starts all season under Frank Lampard at Stamford Bridge, playing just 211 minutes of football, and Chelsea are ready to let the 33-year-old leave if the right offer comes in.
Marseille have been interested in the former Arsenal striker since the summer, and are still at the front of the queue.
But Inter Milan’s former Chelsea manager Conte is also interested and the Italian club are set to compete with Marseille for Giroud.
The France World Cup winner has been vocal about his lack of game time this season, and even his national manager Didier Deschamps has expressed his own worries over Giroud’s lack of action.
Giroud is worried that with Euro 2020 looming next summer, his lack of game time at club level could prevent him playing in what is likely to be his last major tournament finals for his country.
Inter are ready to offer Giroud, who worked under Conte at Stamford Bridge, an 18-month contract.
Chelsea are thought to be asking around £6million for a player with less than six months left on his current deal.
Lampard was forced to outline his stance over Giroud last month, and praised his attitude to being on the sidelines.
He said. “I love his professionalism.
“He was bang on when he spoke to me and with his quotes when he was away with France.
“He shouldn’t be happy and accept not playing.
“That’s what good players do. I think, as I said to Oli, he will get his games and be a big influence for us.”
