Vlasic, 22, is regarded as the best player in the Russian league and is attracting plenty of attention.
The Italian club are reportedly willing to pay €20m, but Zenit are ready to meet CSKA’s valuation of €25m.
According to Jutarnji list, citing the Russian media, Zenit have taken ‘concrete steps’ towards signing Vlasic.
Zenit believe that Vlasic would help them take big steps forward in the Champions League.
Vlasic is tired of waiting for CSKA to build a team that can compete with Zenit for the Russian league title.
CSKA finished 22 points behind Zenit last season and the Saint Petersburg club are already four points clear at the top after four games of the new campaign.
The Muscovites don’t want to sell Vlasic to a rival, but Zenit is by far the richest club in Russia.
Vlasic has already shown his class this season, scoring two goals in two substitute appearances after recovering from an injury.
His first goal of the season came against Zenit in a 2-0 defeat for CSKA last week.