Cornet is committed to leaving Turf Moor this summer following Burnley's relegation from the Premier League.
Due to a clause in his contract, the Ivory Coast international is available for a knockdown fee of just £17.5million.
Despite playing primarily as a forward for the Clarets - finishing last season with nine goals and two assists - Cornet spent much of his career at former club Lyon operating as a left wing-back.
That versatility is attractive to Chelsea boss Thomas Tuchel as the 25-year-old would offer an alternative option to England ace Ben Chilwell as well as an option higher up the pitch.
Tuchel has been promised half a dozen new signings this window and is working closely with Boehly on the Blues' recruitment drive.
Chelsea leave wanted players in limbo
While Todd Boehly is putting all his energies into adding to his squad, Chelsea's boardroom shake-up has left clubs trying to sign their unwanted stars in limbo.
Boehly has taken a hands-on role in transfer dealings following the departure of recruitment guru Marina Granovskaia.
But one boardroom bigwig from a rival Premier League club told talkSPORT they are struggling to make contact with Stamford Bridge officials to put in an offer for a Chelsea player.
Striker Armando Broja - top of West Ham boss David Moyes's summer shopping list - is among a clutch of players expected to leave West London this summer.
Man United could turn to Tielemans
Arsenal's failure to agree a deal for Leicester midfielder Youri Tielemans has put Manchester United on high alert.
Tielemans was expected to have completed his move from the King Power Stadium to north London by now after his representatives held extensive talks with the Gunners in January.
Arsenal's failure to qualify for the Champions League has prompted a change of heart by the Belgian international, while the Gunners have prioritised a number of other deals, including Gabriel Jesus.
While Erik ten Hag is primarily focusing his spending plans on players he has worked with or come up against in the Dutch league, talkSPORT understands the new United boss is a big fan of Tielemans.
The 25-year-old is out of contract next summer so Leicester either need to cash-in now or convince him to sign an extension.
Wan-Bissaka fighting for United future
Aaron Wan-Bissaka is determined to show Man United manager Ten Hag he has a future at Old Trafford.
As well as bringing in new faces, part of the Dutchman's remit upon taking the United job was to cleanse the squad.
Wan-Bissaka's days looked numbered after losing his place to Diogo Dalot at the back end of last season, with old side Crystal Palace keen to re-sign the right-back on loan.
But the £50m man has been putting in extra training hours during his summer break to ensure he is in the best possible condition to play Ten Hag's high-intensity football.
Ten Hag is said to have been impressed with Wan-Bissaka's attitude and is likely to give him the chance to prove himself in pre-season.