Gonzalez, who is also a vice-president of CONMEBOL, the governing body for South America, said it would want at least 14 places at the finals for the two regions combined before accepting the proposal.
CONCACAF represents North and Central America as well as the Caribbean.
The FIFA Council is due to vote on Tuesday whether to increase the number of teams at the finals from the current 32 to either 40 or 48 from 2026. FIFA will decide at a later date which regions will be awarded the additional slots.
CONMEBOL currently has four-and-a-half places at the World Cup for its 10 members while CONCACAF, which has 35 FIFA members in its ranks, has three-and-a-half places.
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"There is a suggestion from Gianni Infantino to unify the CONMEBOL and CONCACAF qualifiers," Gonzalez told the Venezuelan sports daily Meridiano.
"This would have support if they gave us more places. At the moment, we have seven between the two confederations, plus two half places," he said.
"If this went up to 14, similar to what Europe has for more or less the same number of teams, the idea would catch on on the continent."
FIFA could not immediately be reached for comment. Europe currently has 13 places for 55 teams, plus one for 2018 World Cup hosts Russia.
CONCACAF is also a leading contender to host the 2026 World Cup, possibly with a joint bid involving at least two out of the United States, Canada and Mexico.
Gonzalez also said there was "a spirit" in the region in favour of holding a repeat of last year's Copa Centenario in 2020, but with 24 teams instead of 16.
The Copa Centenario, which celebrated the Copa America's 100th anniversary, was a special tournament in addition to the regular Copa America.
The Copa America is played every four years in the year following the World Cup and traditionally features 10 teams from CONMEBOL and two from CONCACAF.
The Centenario, however, took place in the United States and featured six teams from CONCACAF plus the 10 from South America.
CONCACAF also has its own biennial tournament, the Gold Cup, staged in odd-numbered years.
Gonzalez said officials were in favour of another extra tournament in 2020, with a similar makeup to the Centenario but under a different name and with the format increased to 24 teams.
"Obviously it wouldn't be called Centenario," said Gonzalez. "Our Copa America would continue to be played as usual."
Such a tournament may face opposition from European clubs, where many of the region's top players are based.
(Writing by Brian Homewood in Berne; Editing by Toby Davis)
