Bilic's Hammers defeated the Gunners at the Emirates Stadium on the opening day of the Premier League and Mamic was keen to get some inside info from his fellow Croatian.
"Yes, I have spoken to Slaven Bilic, he gave me some advice," Mamic told Goal.com.
"This is great reward for me as a coach and for our team. We are aware of the reality and quality of our opponents, but with fanatic fight we can achieve something."
Zagreb host the Gunners at the Maksimir Stadium on Wednesday night.