The 23-year-old Czech Republic international has played at Sparta Prague for the past three seasons, but is now wanted by the Amsterdammers.
Grygera can play both at right back and as a central defender, and De Telegraaf reports that Ajax want to sign the player before the week is out.
Grygera has been part of the Czech national team since the end of 2001 and he started in the European Championship qualifier with Holland on March 29.
Ajax will face competition for his signature as Juventus and Valencia are also interested in the defender. Ajax also hope to complete the transfer of Rennes defender Julien Escude this week.
