Chelsea have turned to Leandro Paredes as a replacement for Cesc Fabregas.
The Evening Standard believes the Zenit star is now the man they want to add competition in midfield.
But the Blues opening bid of £26.8 million and bonuses is seen as too low.
It is likely it will be rejected by Zenit, as it is the same figure they paid to get the player from Roma in 2017.
The Russians will only sell the 24-year-old central midfielder if they can make a tidy profit.
It means Chelsea will have to stump up close to double their initial offer for a realistic chance at signing the player this month.