Crystal Palace's proposal is worth €10m as a fixed fee, with performance-related add-ons taking the total package to around €17m, according to Alfredo Pedullà – nearly double the roughly €9m Everton were previously reported to have been willing to pay for the Sweden Under-21 international.
Torino held firm and turned the bid down without hesitation, mirroring their response to Everton's earlier interest, with ToroNews suggesting the growing pull from England is itself a sign of how highly the Serie A club rate the 21-year-old's long-term potential.
Njie has struggled to nail down a regular starting role in Turin, scoring once in 15 Serie A appearances last season having managed the same return in 16 games the campaign before, and has featured 35 times for Torino's first team in total since progressing through the club's academy after arriving from Sweden in 2021.
He impressed at youth level across Torino's Under-17s, Under-18s and Under-19s sides before breaking into senior football, and is under contract until 2029, handing the Italian side a strong negotiating position; Torino have already knocked back an offer from Anderlecht for the forward earlier in the window.
Palace's interest comes as new head coach Pierre Sage looks to add further attacking depth at Selhurst Park, with the club having made only one signing so far this summer in centre-back Oscar Mingueza from Celta Vigo.
Torino's stance suggests any deal for Njie is likely to require a significantly improved package before talks can progress, though TuttoSport and Pedullà both note that Palace's willingness to go beyond Everton's valuation shows the level of their interest in the Torino academy graduate.
Everton's own pursuit dates back to June, when the Merseyside club held talks with the player's representatives, but a reluctance to move beyond their initial figure has left them behind Palace in the race for the Sweden Under-21 international, whose stock has continued to rise despite limited first-team minutes.