The 23-year-old Portuguese international has grown into an increasingly important player under Juventus head coach Luciano Spalletti this season, contributing four goals and four assists across 38 competitive appearances. La Gazzetta dello Sport reports that both clubs have taken note of his rising influence in Turin.
Conceição, son of Porto head coach Sérgio Conceição, has three goals and two assists from 15 appearances for Portugal and is contracted to Juventus until the summer of 2030, meaning any deal would require a significant transfer fee.
Liverpool's interest is driven by the need to replace Salah, who has confirmed he will leave Anfield when his contract expires this summer after eight seasons and more than 200 goals for the club.
Multiple targets have been identified, including Bayern Munich winger Michael Olise and PSG's Bradley Barcola, with RB Leipzig teenager Yan Diomandé also understood to have been discussed internally.
Conceição emerged as an additional option following a report from French outlet RMC Sport in March.
United's interest stems from a separate need — the club want to bring in a wide player as part of their summer rebuild under interim manager Michael Carrick and see the Portuguese forward as a profile that fits their requirements.
Whether either club is willing to pay a premium for a player Juventus have under contract until 2030 remains to be seen.