The Napoli skipper would be available for free next summer.
According to a report from the Daily Mail, Chelsea would try to sign the 30-year-old when his contract expires next summer.
Insigne, who has been serving the Partenopei for around a decade, was subject to exit speculation in the summer transfer window.
Despite the interest from top clubs like AC Milan, Inter Milan and Tottenham, Insigne decided to stay put at Napoli.
With less than a year left in his current deal, the Italian forward could seek an exit from his long time club as he had previously hinted that he was open to a new challenge.
Premier League giants Chelsea have now entered the race for Insigne as Thomas Tuchel looks to bolster the attack.
It has also been added that Tuchel is open to selling underperforming stars Hakim Ziyech and Timo Werner.
Werner and Ziyech were signed during Lampard’s reign last year; however, the attacking duo has struggled to adapt to the Premier League.
Insigne is currently relishing the best years of his career after helping Roberto Mancini’s team to Euro Championship glory months ago.
Furthermore, he has kickstarted the new season brilliantly, racking up 2 goals and 3 assists for Napoli, who are the current leaders of Serie A.
Insigne would be looking to spend the prime years of his career in a top club where he can enjoy Champions League football.
Chelsea have recently raided the Serie A market for Romelu Lukaku, whom they signed for a record fee from Inter Milan.
Insigne is a versatile forward who can act as a winger, false 9 and an attacking midfielder. Tuchel can highly benefit from him.
The Italian forward’s stock has hiked up after his brilliant campaign in Euros, and he has long been mooted to ply his trade at Europe’s elite clubs.