West Ham and Tottenham are among the clubs interested in snapping up should the in-form striker decide on a move in January, report Calcio Mercato.
The Italian outlet claims that the London rivals are among a quartet of clubs closely monitoring the Chelsea forward, alongside Italian club Inter Milan and MLS franchise Inter Miami.
Sempre Inter recently claimed that the 34-year-old would be available for just £4.5m which looks a snip after his recent Champions League goal spree.
Giroud had looked to be on his way out of Stamford Bridge, pushed firmly down the peckign order by Tiomo Werner’s arrival in the summer.
The French international had also previously expressed frustration at his lack of game time and with a role as a squad player.
But his stoppage-time winner at Rennes, followed seven days later by his spectacular four-goal haul at Sevilla has put him firmly back in the spotlight, and shown his worth to Frank Lampard.
And Giroud has now reiterated his desire to stay at Stamford Bridge, albeit that would most likely come with a caveat of more game time to show his worth to French international boss Didier Deschamps.
“I had a conversation with Deschamps and he said if the situation stayed like that, I will have to take a decision in January,” Giroud told the official Chelsea website.
“I am pretty sure I can get some more game time and stay at Chelsea because that is what I want. I want to win trophies with Chelsea so basically that’s it.