Brighton have rejected an offer from Al Nassr for winger Kaoru Mitoma worth £54m (€65m) - but the Saudi Arabian club are preparing a new and improved bid.
Time is running out for the Saudi Pro League club to get a deal done, with their window shutting at 8.59pm UK and Irish time on Friday.
It is understood the Japan international is not for sale.
Sky in Italy are reporting that Al Nassr's fresh offer is worth more than £71m (€85m).
Al Nassr won 2-1 on Thursday night against Al Raed in the Saudi Pro League and are now just five points off top spot in third.
They are keen to make a big push to help Cristiano Ronaldo, who turns 40 next month, to win his first Saudi Pro League title.
Mitoma, 27, joined the Seagulls from Japanese side Kawasaki Frontale in 2021 for a reported £2.7m before spending the 2021/22 season on loan at Belgian club Union Saint-Gilloise.
Mitoma made his Brighton debut in August 2022 has since made 92 appearances in all competitions, scoring 18 goals.
Mitoma has played in all 23 Premier League games for Fabian Hurzeler's side this season and has netted five goals.
Al Nassr's move for Mitoma comes after they agreed a £64m deal for Aston Villa striker Jhon Duran.
Al Nassr's deal for Colombia international Duran is part of a new Saudi strategy to focus on singing young and developing players rather than being regarded as a retirement home for ageing superstars.
Sky Sports News' chief reporter Kaveh Solhekol speaking on The Transfer Show:
"Cristiano Ronaldo plays for Al Nassr, who are one of the four clubs in Saudi Arabia owned by the sovereign wealth fund so they are one of the richest clubs in Saudi Arabia.
"Even though they've got Ronaldo, they have not really been challenging for the title. Al Hilal are the best team in Saudi Arabia at the moment so I wonder whether Ronaldo has been putting a bit of pressure on the people upstairs at Al Nassr and saying, 'I want to win more titles and trophies', as he turns 40 next week.
"This is maybe why they're going for top players like Jhon Duran and Mitoma."
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