According to Sky Sport, the club's revised proposal for Kolo Muani will keep the fixed fee at around €35m but increase the add-ons and include a sell-on percentage for PSG, an attempt to close the gap with a French club that has previously valued the striker considerably higher.
The two sides have been negotiating for weeks over a move that would take Kolo Muani back to Turin, where he previously spent time on loan.
Juventus have also stepped up contact with Parma over Pellegrino, with club officials meeting the Emilia-Romagna side to discuss a structured loan. The proposal includes an initial loan fee followed by an option to buy that would become obligatory if Juventus qualify for European competition next season, a formula designed to manage the financial risk of signing the Argentine forward outright.
The Bianconeri's strategy appears to be pursuing both targets in parallel rather than treating them as alternatives, with the club keen to add two forwards of different profiles to support Luciano Spalletti's attacking options as he begins his first full season in charge.
Kolo Muani remains the priority given his pedigree and previous spell in Serie A, while Pellegrino is seen as a younger, longer-term addition who could complement rather than replace any deal for the Frenchman.
Parma, for their part, appear open to negotiating the structure of any deal, though talks are understood to still be ongoing over the precise terms of a potential obligation to buy and the overall valuation of the player.
Pellegrino scored 12 goals and provided one assist across the league and Coppa Italia last season, form that has made him one of the more sought-after young forwards in Serie A this summer.
Juventus are said to be moving quickly to secure him before other suitors enter the race, effectively looking to book the deal even as the finer details are still being worked out. Kolo Muani, meanwhile, remains keen on a return to Turin having previously impressed on loan, though PSG's valuation remains the main obstacle to an agreement.