The Reds reportedly rejected a £150m offer from Al-Ittihad for the 31-year-old last September.
“We know that trophies are what count and we will do everything possible to make that happen next season,” Salah posted on social media.
“Our fans deserve it and we will fight like hell.”
Liverpool won the League Cup in Jurgen Klopp’s final season in charge but missed out on the Premier League, FA Cup and Europa League.
Klopp’s departure after over eight years in charge of Liverpool has raised doubts over the futures of a number of star players, who rose to prominence under the German’s reign.
Virgil van Dijk and Trent Alexander-Arnold are also entering the final year of their contracts.
Former Feyenoord boss Arne Slot was confirmed as Klopp’s successor by Liverpool on Monday.
© Agence France-Presse
Photo: Twitter @AnfieldSector