Terry left Aston Villa at the end of last season.
Terry left Villa at the end of last season, with the Midlands club unable to offer an extension to his initial one-year deal.
But despite rumours the 37-year-old could retire to pursue a career in either coaching or punditry, a market remains on his next playing club.
Derby County, whose new manager is Terry's close friend and former Chelsea teammate Frank Lampard, have long led the betting and remain evens favourites, with Celtic recently appearing behind the Rams at 5/1.
But both Celtic and Aston Villa, who had fallen out of the running, are now 6/1 to become Terry's next club.
The development comes just days after the Egyptian billionaire Nassef Sawiris bought a controlling stake in the Villans, who reports claimed were facing a financial crisis if not.
Could Terry head back to Aston Villa this summer?