The Celtic star is being linked with a move to Russia.
The same publication claimed earlier in the week that the big-spending Russian side were readying a £12 million move for Forrest.
Hoops boss Neil Lennon said on Monday that he isn't for sale and that Celtic want to keep him.
But Lennon will also know that money talks and The Scottish Sun's initial report indicated that the 28-year-old could consider a big-money switch.
Zenit could make the Scot a very rich man, given that he will presumably be offered at least a three-year contract, which equates to around £11 million in wages.
The Bhoys are set to offer him a new contract, but those figures ensure that Celtic will be blown out of the water entirely.
There is plenty of incentive to stay in Glasgow, with Lennon's side being two Premiership titles away from a historic 10-in-a-row.
But that wasn't enough to keep Brendan Rodgers or Kieran Tierney, so it remains to be seen if the Scotland international will be tempted by Zenit's reported offer.
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