The forward, who eclipsed the record previously set by Ruud van Nistelrooy by scoring in 11 consecutive Premier League games, may move to Stamford Bridge next month.
However, given the Blues’ previous New Year signings, there is no guarantees he would replicate the same form with the Foxes over in the capital.
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Here, GiveMeSport rates the club’s last five winter transfer window signings and how they fared.
When Chelsea swooped for Juan Cuadrado a year ago, many believed the Columbian to be the perfect replacement for Andre Schurrle, who joined Wolfsburg.
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However, the former Fiorentina winger struggled to adapt to his new surroundings and returned to Serie A with champions Juventus in the summer.
However, since Jose Mourinho's dismissal as manager, new man Guus Hiddink may be prepared to give the Colombian one last chance to return to London and prove a point to the fans.
Despite allowing him to join Benfica as part of the deal to sign David Luiz in 2011, Chelsea splashed the cash to bring Nemanja Matic back to the club in January last year.
The Serbian, who signed for £21million, has been a big hit at Stamford Bridge and his partnership with Cesc Fabregas was crucial as the Blues eased to the league title in May.
Though his performances have been inconsistent this term, the 27-year-old still represents good business given his solidarity and composure in midfield.
Whether or not he improves will also have a big impact on the club’s pursuit of a top four finish.
The case of Mohamed Salah had been a difficult one for Mourinho to crack.
Yet after finding starting opportunities limited, he was loaned to Fiorentina as part of the Cuadrado deal where he proved to be a revelation.
The 23-year-old is currently spending this campaign with Roma, where he has five goals in 13 league games, but it is still unknown whether or not he has a future at his parent club.
Rating 7/10 (for form in Italy rather than London)
Chelsea beat the likes of Manchester United and Liverpool to sign Kurt Zouma from St-Etienne in January 2014.
And the youngster, though raw and unpolished in places, looks like he will one day be the perfect John Terry replacement.
The 21-year-old has also proven his versatility by operating in midfield, and he was one of the standout performers as the club beat Tottenham to win the Capital One Cup in March.
Zouma has the potential to be a future Blues captain and his terrific performance against Porto helped the club through to the knockout stages of the Champions League.
Demba Ba’s arrival in the winter window of 2013 came with Fernando Torres misfiring and Juan Mata their biggest goalscoring threat.
After helping Newcastle finish fifth the previous campaign, his goals made him one of the most prolific forwards in the top flight.
However, he never quite hit the same heights during his brief stint at Stamford Bridge and has since rebuilt his career away from England.
He is currently in China with Shanghai Shenhua and, if recent reports are to be believed, could be joined by Wayne Rooney.
Chelsea fans: Who would you like to see signed in the January transfer window? Give YOUR opinion in the comment box below!