The club is under new ownership this month after Claudio Lotito, who also owns Lazio, finally made the sale.
New director general Walter Sabatini is hard at work and Il Mattino newspaper claims he has struck a deal with veteran hitman Costa.
The 33-year-old is a free agent after his experience with Atletico Mineiro and had also been linked with Newcastle United.
However, it’s reported he has agreed personal terms with Salernitana instead, as Sabatini had already met with Costa when working for Bologna last season.
It would form a spectacular attacking partnership with Franck Ribery, who already joined Salernitana over the summer.
There are also reports that Kaio Jorge could join Salernitana on loan from Juventus after the arrival of Dusan Vlahovic from Fiorentina.
It would give the young Brazilian more playing time to get accustomed to Serie A football.
Cagliari are also interested in a potential loan, especially if Nahitan Nandez were to go the other way to Juve.
Meanwhile, Salernitana have officially signed Pasquale Mazzocchi from Venezia and Luigi Sepe from Parma.
Diego Costa alla Salernitana, è fatta:
il super bomber in coppia con Ribery https://t.co/71KXxCbKf7
— Il Mattino (@mattinodinapoli) January 25, 2022