The Eredivisie champions made an unsuccessful bid for the Icelandic striker last month, thought to be in the region of €3.5million (?3.1million).
The Godenzonen reportedly want to sign Sigthorsson, whose contract at AZ expires next summer, on a four-year deal.
Ajax technical director Danny Blind hopes to continue talks over the 21-year-old in the coming days.
"We will seek talks with AZ this week to get back in," Blind told Voetbal International.
"No one will benefit if this turns out to be a lengthy matter."
Sigthorsson, a youth product at AZ, broke into the first team last season and made an instant impact, notching up 32 league appearances and scoring 15 goals.
He has been linked with a host of Premier League clubs this summer, with Newcastle and Bolton among those reportedly monitoring the youngster.
Source: Team Talk
Source: Team Talk