The Blues have lost Ben Chilwell for the rest of the season to a cruciate ligament, leaving them short of the depth on the left flank where Marcos Alonso has started 12 of the last 14 games in all competitions.
Perisic has operated as left wing-back for Inter Milan this season and, according to the Mirror, Chelsea see him as the ideal candidate to provide cover and competition for Alonso.
Inter Milan winger Ivan Perisic has emerged as a target for Chelsea this month
The European champions were hoping to sign Everton defender Lucas Digne to bolster their left-back options in January, but could not agree a loan deal for the Frenchman.
Digne eventually moved to Aston Villa last week for £25 million, prompting Tuchel to recall Kenedy from his loan at Flamengo.
The Brazilian has been a Chelsea player since 2015 but has failed to establish himself as a regular at Stamford Bridge and Flamengo was his fifth loan spell.
Chelsea lost both their starting full-backs to injuries and are short of options on the flanks
Thomas Tuchel is eager to bolster his options at left-back in the January transfer window
Perisic has played 230 games for Inter Milan, scoring 49 goals and setting up a further 42, since joining from Wolsfburg in the summer of 2015.
The 32-year-old has six months left on his deal and is understood to be happy to sign a new contract with the reigning Serie A champions, but the two parties remain distant.
Earlier this week, Gazzetta dello Sport reported Perisic wanted to sign a three-year deal on a salary higher than his current one, while Inter Milan would prefer him to pen a two-year deal on lower wages.
Should Inter and Perisic fail to reach an agreement, the Serie A champions could look to sell him in January instead of losing him for free in the summer.
The Croatia international has only another six months left on his deal at the San Siro
Meanwhile, the Nerazzurri’s president Steven Zhang told Italian outlet Tuttosport this week that signing a long-term replacement for the Croatia international was among the club’s priorities.
Perisic has also previously played as right wing-back and his versatility could solve another issue for Tuchel, who has lost Reece James and Trevoh Chalobah to injuries.
The former sustained a hamstring injury against Brighton on December 27 which is expected to keep him out for another four to six weeks, while the latter could be unavailable for a few weeks after aggravating a hamstring injury against Liverpool on January 2.
Source: Daily Mail