The Russian international joined the Emirates Stadium outfit at the beginning of February for £15 million, and enjoyed an explosive start to his Premier League career, netting six league goals in 12 appearances, including four against Liverpool at Anfield.
However, the diminutive playmaker has recently revealed his shock and horror at the hefty amount of tax being deducted from his salary.
And the news is thought to have prompted the 28-year-old's former club - who are backed by the largest oil and gas company in the world - to plot a big-money move to lure Arshavin back to his homeland.
Zenit are currently languishing in sixth place in the Russian Premier League, losing three of their last five matches.
"The bosses of the St Petersburg club intend to make Andrey a very thoroughly thought out offer which can motivate him to return home," said Sport Den Za Dnem, quoting a source.
"He has started his career at Arsenal brilliantly but that is not an obstacle for negotiations - on the contrary money is a good reason to begin them. Zenit need reinforcements."
Zenit St Petersburg have refused to comment on the speculation.
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