The Inter Milan star has only six-months left on his current contract at the San Siro, meaning he is able to arrive at Stamford Bridge in a cut-price deal or on a free.
The Blues have lost full-back Ben Chilwell for the rest of the season due to a cruciate ligament injury, which has left Tuchel desperate for more depth with only Marcos Alonso able to operate on the left flank.
Perisic has primarily operated as a left-wing-back under Inzaghi so far this season, and reports suggest that Tuchel views the Croatian as a viable option this winter.
The reigning European champions were initially in the race for French defender Lucas Digne, who has since left Everton to sign for Steven Gerrard’s Aston Villa.
Perisic is understood to be very happy to stay at Inter Milan and wants to renew his contract with last season’s Serie A winners, but talks have reportedly stalled as the player seeks a three-year deal with higher wages - terms that the club do not wish to agree to.
The 32-year-old has featured 230 times for Inter Milan, notching 49 goals since he arrived from German side Wolfsburg in 2015.
If both parties fail to agree on any contractual terms, the club are prepared to cut their losses and allow Perisic to leave in January.
The Croatian has previously operated as a right-wing-back option too, making his versatility an attractive attribute for Tuchel who has lost the likes of Reece James and Trevoh Chalobah to injuries.
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