With the Blues expected to miss out on Jules Kounde - who is edging closer towards a move to Barcelona - the club have turned to RB Leipzig defender Mukiele as a possible alternative.
The Frenchman was expected to join Ligue 1 champions Paris Saint-Germain after a £13million deal was reportedly agreed.
However, Chelsea are said to have submitted a late offer of their own as they look to hijack the signing.
Since his move from Montpellier, Mukiele has made 145 appearances for RB Leipzig and was even capped by France.
According to FootMercato reporter Santi Aouna, Chelsea are expected to sweeten the deal for the defender by including Timo Werner as part of the move.
While manager Thomas Tuchel did play down reports regarding Werner's possible departure, he was clearly irked by the striker's suggestion that he would be "happy everywhere" as long as he plays and scores goals.
The Blues boss said: "I would be very happy as a young guy having a contract at Chelsea Football Club. I would be one of the happiest people on the planet."
The German manager then hit back at Werner's lack of game time, adding: "Show quality, take your place and defend your place. I would be one of the happiest people on the planet having a contract with Chelsea. If he said this, I do not understand."
Werner has struggled since making his switch to the Premier League, scoring 23 goals in 89 games.
What's more, the German international also pockets the highest wage at the club, earning a reported £272,000 per week.
Werner arrived in London from RB Leipzig, where he scored 95 goals in 159 games across all competitions.