Auckland's amateurs will open the competition against the still-undecided J-League champions on December 8 and following Thursday's draw, the winners face Monterrey three days later.
Tribulietx had been hoping to avoid the Confederation of North, Central American and Caribbean Association Football (CONCACAF) champions after their 3-0 mauling by Mexico's Atlante in 2009.
"CF Monterrey is a fantastic team but we want to focus on the first game. Any of the teams would have been difficult but Monterrey is the best of that trio," Tribulietx told the club website, www.aucklandcityfc.com.
"Two years ago we played Atlante and they were top-class."
In the meantime Tribulietx is concentrating on Auckland's remaining domestic and Oceania league games before sizing up the Club World Cup and naming his squad next Thursday.
"We have domestic and Oceania matches to play yet so our focus remains on Hekari United and Manawatu – and then we will worry about the J-League champions," he said.
"There will be some tough decisions to make before we leave and one of those will be naming the squad," the coach added.
"We’ve won five games since the season started and the competition for places has been intense. But I think we will be in a strong position to name our group by the end of next week."