Dennis Lachter told the paper that the club's president had called him on Monday to inform him that Arshavin, one of the stars of the recent Euro 2008 tournament, would remain with the Russian champions.
Zenit, owned by state-run energy giant Gazprom, had earlier rejected bids from Barcelona and Tottenham as "too low." When Tottenham eventually offered to meet Zenit's asking price of some $36 million they were told it was too late. Zenit were also dissatisfied with the London club's offer to pay the sum in installments over four years.
However, Lachter said Alexander Dyukov had told him that if Tottenham were still interested when the transfer window opened again on New Year's Day then talks could resume.
Zenit begin their debut Champions League campaign this month. They face Real Madrid, Juventus, and BATE Borisov of Belarus in the group stages. Zenit also won the Super Cup on Friday, beating Manchester United 2-1 in Monaco.