Starsport reported last week that Brendan Rodgers was interested in the 23-year-old Ukranian, but the Anfield boss ended his pursuit after being put off by Kyiv's asking price.
Kyiv value Yarmolenko at £23 million, and whilst Liverpool's offer for the former Desna Chernihiv star is not public knowledge, it's understood their bid fell well short of Kyiv's valuation.
The young hitman remains interested in a move to the Premier League, though Zenit St Petersburg could yet rival Liverpool and revive their interest in the player when the transfer window reopens in January.
Liverpool boss Rodgers had a very productive transfer window, even without the addition of Yarmolenko, bringing the likes of Iago Aspas, Simon Mignolet, Tiago Ilori and Victor Moses to the club.
And the Anfield side have enjoyed similar success on the pitch too, sitting top of the Premier League with maximum points and three consecutive 1-0 wins, the latest being Sunday's success over Manchester United.