Conceição joined Juventus permanently last summer, signing a contract running until 2030, and contributed three goals and five assists in 31 league appearances, 27 of them starts, last season.
Liverpool and Manchester United were both credited with interest in the Portuguese winger earlier this year, but it is Liverpool who have now moved to open discussions with his representatives, according to Italian reports.
Liverpool are also chasing a replacement for Salah in Paris Saint-Germain's Bradley Barcola, and Conceição is understood to represent an alternative option should that pursuit prove difficult to complete. Juventus are demanding a fee of around €50 million for the 23-year-old, having paid around €40 million to sign him from Porto, and are said to be unwilling to let him leave for anything less given his importance to Luciano Spalletti's squad.
Conceição, who previously played for Porto and Ajax earlier in his career, has become a regular starter for Portugal, scoring four goals and providing three assists in 21 senior caps. His versatility across both flanks and his physical, direct style of play have made him an increasingly attractive target for Premier League clubs, with Liverpool viewing him as a genuine option to strengthen their attack regardless of how the Barcola situation develops.
Juventus, for their part, have shown no willingness to negotiate below their asking price, leaving Liverpool with a decision to make over whether to test that resolve with a formal bid before the transfer window closes.
RB Leipzig have also begun monitoring Conceição's situation as a possible attacking option should they lose Yan Diomandé, whose move to Real Madrid is close to completion, adding a further layer of competition to any potential deal. For now, no official offer has reached Juventus from any interested club, and the Portuguese himself has previously insisted publicly that his focus remains on Turin.
Whether that stance holds is likely to become clearer in the coming weeks, with Liverpool's need for attacking reinforcements only growing more urgent as the new Premier League season approaches.