According to journalist Sacha Tavolieri, Hull City have recently made contact over the 23-year-old centre-back, requesting terms for a possible deal as they look to add further defensive options ahead of their return to the Premier League.
The newly promoted club face competition from elsewhere in the market, with Sunderland, Strasbourg and FC Copenhagen also said to be exploring a move, while interest from Spain earlier in the summer is reported to have since cooled.
Adjei, a Ghana international, left Swedish top-flight side Hammarby for Lorient in January 2024, a switch he made permanent later that year for a reported fee of around €5.7m, and holds a contract with the French club running until the summer of 2028.
His first season and a half in France were disrupted by a serious ankle injury that kept him out for close to a year, but he has since become an important figure in Lorient's defence, making 15 league appearances last season, nine of them starts, as the club finished tenth in Ligue 1.
Lorient are said to be reluctant to sanction a sale, with new head coach Alexandre Dujeux having been impressed by the defender throughout pre-season and viewing him as an important part of his plans for the campaign.
Hull have already been busy elsewhere in the market this summer, having agreed the signing of Sweden winger Elliot Stroud from Mjällby, part of a wider push to strengthen the squad ahead of the club's first Premier League campaign since 2017.