When the Ivory Coast international departed AC Milan for Camp Nou on a free transfer earlier this year, he was expected to hold down a regular spot in the starting lineup.
However, the 25-year-old has been provided with just five starts and eight substitute appearances having failed to dislodge Sergio Busquets from his long-term role in the centre of the pitch.
Reports have recently emerged that Barcelona officials would be prepared to cash in on Kessie should they receive a suitable offer at the turn of the year.
Having not been required to pay a transfer fee for the player, Barcelona would significantly boost their FFP position by generating a substantial fee.
According to transfer expert Fabrizio Romano, Kessie's agent is currently insistent that there will be no change of clubs at the midway point of the campaign.
Nevertheless, Inter Milan are being heavily linked with an approach for Kessie, whether that be on a temporary or permanent basis, with the Italian giants hoping that their rivalry with his former club will not become a factor.
According to Relevo, Napoli are contemplating whether to rival Inter for Kessie's signature in the January transfer window.
Napoli are currently on course to win their first top-flight crown in 33 years having opened up an eight-point lead at the top of the standings.
Luciano Spalletti's side have recorded 13 wins and two draws from 15 matches, while the club have a settled number of options in the middle of the pitch in Andre-Frank Zambo Anguissa, Stanislav Lobotka, Piotr Zielinski and Tanguy Ndombele.
However, the report claims that Napoli are ready to push for a loan deal in a bid to further strengthen their bid for silverware during the second half of the season.
The report adds that Kessie, should he depart Barcelona in January, would prefer to move to an Italian club, although his representatives are said to have informed Barcelona that his priority is to stay in Spain.
Kessie is allegedly focus on making more of a sustained impact once Barcelona resume their schedule on New Year's Eve versus Espanyol.