The Clarets were interested in acquiring the services of the player four years ago and had a total of six bids rejected by Brighton then.
Stephens even handed in a transfer request in an attempt to force his way out of the club on that occasion, but the Seagulls refused to sanction his departure.
Now Burnley have revived their interest in the former Southampton loanee and have tabled an offer as they look to sign him from Brighton.
While it remains to be seen how much money the Clarets have offered their league rivals, the chances of a deal being struck are higher than four years ago.
Stephens has entered the final year of his contract with Brighton, who might prefer to bank some money for the player than losing him for free next summer.
The English midfielder’s game time at the Amex this season is also likely to be significantly less, with Yves Bissouma and Steve Alzate the preferred midfield pairing at the club.
The Seagulls have Davy Propper and Jayson Molumby as midfield options as well, increasing the chances of Stephens having a limited role in Graham Potter’s plans.