The 22-year-old has spent almost a year in West London, having departed Monaco in a £32.7m deal to join the Blues on a lengthy seven-year contract until the summer of 2030.
Badiashile made 11 appearances for Chelsea during his first half-season at the club, scoring once in a 3-1 win over Bournemouth before entering the treatment room with a hamstring problem.
The France Under-21 international was still working his way back from his severe affliction when the 2023-24 season kicked off, and he was forced to wait until November to make his first appearance under Mauricio Pochettino.
Since returning to full fitness, Badiashile has featured regularly in the heart of the Blues backline, starting four of their last five Premier League matches and also netting in an EFL Cup win over Blackburn Rovers last month.
With former Monaco teammate Axel Disasi being shifted across to the right to cover for injured captain Reece James, and Levi Colwill deputising on the left for the stricken Marc Cucurella and Ben Chilwell, Badiashile is expected to continue earning regular starts alongside Thiago Silva over the festive period.
However, a report from Foot Mercato claims that the 22-year-old is being eyed for a swift return to Ligue 1 in the upcoming window, as Lyon want to take him on loan for the second portion of the campaign.
The seven-time French champions have endured a disastrous start to the new term and sit 16th in the Ligue 1 rankings, but they have won their last two matches against Toulouse and Monaco.
The report states that Lyon owner John Textor will have a budget of around £43m to spend in the January transfer window, and Badiashile is one of two Premier League-based targets for Les Gones, who are also tracking West Ham United's Nayef Aguerd.
A deal for the former Rennes man is viewed unrealistic, though, as he is happy at the London Stadium and is also due to represent Morocco at the Africa Cup of Nations next month, forcing Lyon to turn their attention elsewhere.
Chelsea and Lyon are understood to enjoy a positive relationship thanks to the sale of Malo Gusto to the Blues in January, while Portuguese attacker Diego Moreira went in the opposite direction this summer.
However, Les Gones may be fighting a losing battle to prise Badiashile away from Stamford Bridge, as the defender has no intention of leaving the Blues, who would also be reluctant to part ways with him.
Badiashile - who has also been linked with AC Milan - is seen as an integral part of Chelsea's future amid uncertainty surrounding Silva's situation, as the Brazilian turns 40 next year and will enter the final six months of his contract in January.
Nevertheless, the Blues could still part ways with two out-of-favour defenders in Malang Sarr and Trevoh Chalobah, neither of whom have played a game this season, although the latter has been nursing a problematic thigh injury.
Sarr and Chalobah's exits could tempt Chelsea into moving for a new centre-back next month, and the West London giants are believed to be keeping an eye on Torino's Alessandro Buongiorno.