The current kings of Europe will enter the competition to be held in Japan in December at the semi-final stage along with Copa Libertadores holders Corinthians of Brazil
The Mexican club qualified for the competition by winning the Concacaf Champions League for North and Central American and Caribbean teams, while the Asian tournament remains at the quarter-final stage.
Monterrey and the Asian Champions League winners will meet in the quarter-finals of the Fifa competition to determine the world's top club, which will be held in Japan over 10 days in December, to earn the chance to face the Blues.
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Saudi Arabian teams dominate the list of eight contenders still competing for the Asian Champions League. Al-Ittihad, Al-Hilal and Al-Ahli are all still in the tournament.
Sepahan of Iran, Guangzhou Evergrande of China, Adelaide United of Australia, Bunyodkor of Uzbekistan and Ulsan Hyundai of Japan also remain in contention.
In the other side of the draw, the winners of the J.League - Japan's top flight - will qualify as hosts and face Auckland City, who won the OFC Champions League in Oceania, in a play-off.
The winners of that match will face the AFC Champions League winners of Africa, with that tournament currently at the semi-final stage, in the quarter-final. The victors there will go on to face Corinthians, winners of the Copa Libertadores in South America, in the semi-final.
The African teams still in contention for a place in Japan are Mazembe of the Democratic Republic of the Congo, Esperance of Tunisia, Sunshine Stars of Nigeria and Al-Ahly of Egypt.