Chelsea and Zenit's valuations for Leandro Paredes are currently €10 million (£9m/$11m) apart after the Blues were asked to increase their offer for the midfielder to €40m (£36m/$46m).
Goal understands the Premier League club's initial approach for Paredes was €30m (£27m/$34m), and the closeness of the two valuations means that there could soon be a positive outcome for the Argentina international.
Paredes, who showed up to conduct medical tests on Monday with Zenit after a winter break period in the Russian Premier League, is seen by Chelsea boss Maurizio Sarri as an ideal type of player to come in and deputise for Jorginho.