Zenit St Petersburg are desperate for Paredes to stay.
But the reports claim they also fear their star will go on strike to force through a move to Stamford Bridge this month.
Russian leaders Zenit are now looking for a replacement for Paredes in case he joins Chelsea.
Paredes has netted 15 goals and assisted 10 more in his 61 appearances for Zenit.
Chelsea target Paredes shows off stunning skills for Zenit
Chelsea transfer news: Maurizio Sarri wants to add Leandro Paredes to his squad (Image: GETTY)
He joined in 2017 from Roma for an initial £21m.
Chelsea boss Sarri is keen to bolster his squad this month with a striker high on the agenda.
The likes of AC Milan forward Gonzalo Higuain has been linked with the Blues.
“As I said before, the club knows my opinion, and in my opinion we need two players,” Sarri said after the win over Newcastle.
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Chelsea transfer news: Leandro Paredes would be the replacement for Cesc Fabregas (Image: GETTY)