The Moroccan midfielder has established himself as a key member of Guus Hiddink’s squad, but he is, nonetheless, expected to leave the club in the near future.
Anzhi officials are willing to part ways with the 28-year-old in order to accommodate new signing Willian.
Lifesports understands that a €20 million price tag has been placed on the Morocco international, with Anzhi chiefs hoping Boussoufa will leave before the transfer window in Russia closes.
Liverpool and Zenit have so far been keeping tabs on the experienced midfielder, but it remains to be seen whether they will be prepared to splash the cash on the Moroccan.
Mbark Boussoufa joined Anzhi in a €6.5 million deal from Anderlecht in March 2011 and has since made 56 Russian Premier League appearances for the club, scoring 10 goals in the process.