Vlasic, 22, is considered one of Europe’s most promising youngsters and is primed for a move to a top league.
In a recent meeting, Napoli owner Aurelio De Laurentiis, coach Rino Gattuso and sporting director Cristiano Giuntoli agreed that an attacking midfielder was needed.
Vlasic is at the top of their list, with Giuntoli already making contact with his camp through intermediaries.
CSKA are open to selling Vlasic if an interesting bid arrives and value him at around €22m.
Napoli plan to offer €20m, perhaps adding future bonuses to convince the Russian club.
Vlasic joined CSKA from Everton and still has four years remaining on his contract.
CSKA later made his move permanent for an undisclosed fee, believed to be around £14m.
Vlasic has flourished in the RPL and has a record of 21 goals and 14 assists in 69 appearances.
The 11-time Croatian international is a versatile attacking midfielder, capable of playing behind the striker and on both wings.