The 34-year-old former Arsenal player has received an offer to stay with Zenit in another role but has yet to decide on his future.
Zenit's website (www.fc-zenit.ru) said Arshavin and team mate Anatoly Tymoshchuk had brought the club great success and both had been offered jobs "within the club's system".
Arshavin, who scored 17 goals in 74 matches for the Russian national team, has not decided what his next move will be.
"I have mixed feelings and emotions at the moment," the newspaper Moskovsky Komsomolets quoted the player as saying.
"I don`t want to speak about what has not happened yet and what is not certain to happen in the future."
Arshavin joined Arsenal from Zenit in 2009 and played 105 Premier League matches for the London side.
In February 2012 the Russian returned to Zenit and in his final season he helped the club to win the Russian Premier League title.
(Reporting By Dmitriy Rogovitskiy; editing by Clare Lovell)
