Les Gones were said to have been weighing up a mid-season loan move for the former Monaco man, who has endured an injury-hit start to his Stamford Bridge career.
Badiashile arrived in West London from Monaco in January, but he missed the first couple of months of the 2023-24 campaign with a hamstring injury, which also cut his first half-season short.
The France Under-21 international has also faced stiff competition from Axel Disasi and Thiago Silva for starts at centre-back, which has now intensified owing to Mauricio Pochettino's switch to a four-man rearguard system.
Nevertheless, football.london claims that Lyon are not looking to bring Badiashile back to his homeland next month, and the 22-year-old also has no intention of departing Stamford Bridge so soon.
Badiashile - who is under contract at Chelsea until the summer of 2030 - has capitalised on his teammates' injuries to become a regular fixture in the Blues' backline, starting four of their last five Premier League contests.
The Frenchman has often formed an alliance with 39-year-old Silva, given Disasi and Levi Colwill's need to cover for the stricken Reece James, Ben Chilwell and Marc Cucurella out wide.
With Wesley Fofana and Trevoh Chalobah also nursing long-term knee and thigh issues respectively, Badiashile and Silva will continue as Pochettino's first-choice central pairing over the busy festive period.
Badiashile has been restricted to just 16 appearances in a Chelsea shirt over the past 12 months, but he has amassed two goals and one assist for the club in that time, netting on his first appearance of the campaign against Blackburn Rovers in the EFL Cup.
The ex-Monaco man has since completed the full 90 minutes in Premier League meetings with Brighton & Hove Albion, Newcastle United, Everton and Sheffield United, helping the Blues keep a clean sheet against the latter in a 2-0 success on Saturday.
The Blues will now be taking on Newcastle United on Tuesday evening with a place in the EFL Cup semi-finals on the line, where Badiashile will be expected to hold his spot in defence amid Chelsea's injury crisis.
While the 22-year-old will be going nowhere in January, Chelsea have two unwanted defenders on the transfer list in Chalobah and Malang Sarr, the former of whom has not made a single appearance this term due to a thigh issue.
Sarr has also not been seen in a Chelsea shirt this season, although his absence has been purely for tactical reasons, as he was left out of the Blues' Premier League squad for the 2023-24 campaign.
Pochettino's side could try to bolster their backline in January if one or both of Sarr and Chalobah leave, with Torino's Alessandro Buongiorno believed to be on their radar.