The 25-year-old has spent the last three years at the Amex Stadium since joining from Brentford for around £14m in 2019.
Maupay has scored 27 goals and registered seven assists in 109 appearances for the Seagulls across all competitions and has been the club's top scorer in each of the last three Premier League seasons, netting eight times in 32 top-flight games last season.
While Maupay is regarded as one of the main striking options under Graham Potter, his long-term future on the South Coast is believed to be uncertain as he has now entered the final year of his contract.
According to The Athletic, Brighton now have a decision to make as they have recently received a €17.6m (£15m) offer from Salernitana.
The Italian side were promoted to Serie A for the first time in 23 years last season, and although there were fears of an immediate return to the second tier in 2021-22, they eventually survived after finishing just one point above the bottom three.
Salernitana, who have the likes of French veteran Franck Ribery on their books, have already spent around £20m on new recruits this summer, but they are keen to reinforce their frontline and have identified Maupay as one of their top targets.
Maupay faced competition from Danny Welbeck and Leandro Trossard for a place in Potter's starting lineup last season and the Frenchman's game time could be limited further in 2022-23 following the arrivals of Deniz Undav and Julio Enciso.
Undav was signed by Brighton in January from Belgian Pro League outfit Union SG, who are co-owned by Seagulls chairman Tony Bloom, before returning to the club on loan for the second half of last season.
The 26-year-old striker finished the 2021-22 league campaign as the top scorer in the division with 25 goals in 33 appearances.
Eighteen-year-old Enciso, meanwhile, has joined Brighton this summer for around £10m from Paraguayan side Club Libertad, where he netted 21 times in 68 appearances across all competitions.
Brighton have also added winger Simon Adingra to their ranks for around £7m this summer, while they are reportedly interested in signing free agent Florian Grillitsch, who left Hoffenheim last month upon the expiration of his contract.
The Seagulls have recouped around £30m this summer from the sales of Yves Bissouma and Leo Ostigard to Tottenham Hotspur and Napoli respectively, while they are reportedly in talks with Manchester City over the potential sale of Marc Cucurella who is valued at £50m.