Liverpool reportedly rejected an offer worth up to £150 million ($189 million) for the Egyptian this week from Al-Ittihad.
Jurgen Klopp has shot down any suggestion the Reds could entertain a bid for Salah, who signed a new three-year deal at Anfield last year.
The Premier League transfer window closed on Friday, but Saudi clubs can still add to their squads before September 7.
"It is football, everyone is talking. We are really happy that he has stayed," said Szoboszlai after netting his first goal for the club.
"We are of course speaking between each other but he wants to stay, he wants to be here and be with us.
"We are really happy. We need people in the team like him."