New boss Unai Emery has worked with the player at Spartak and he is eager to lure him to Ramon Sanchez Pizjuan.
The Russian giants are ready to cash in on the former Netherlands international, but the problem is that Anderlecht have the first option on the experienced midfielder.
De Zeeuw is currently on loan with the Belgian giants and they can exercise the clause to make the transfer permanent at the end of the campaign.
It is highly unlikely that will happen though, considering that the 29-year-old made just four substitute appearances for Anderlecht since arriving at the club in January.
De Zeeuw has a contract until June 2014 at Spartak Moscow, and is valued at around €3 million. Before he was loaned to Anderlecht, the midfielder featured in just 25 league matches for Spartak.