The FIFA boss will submit his latest proposal at a FIFA Council meeting in Zurich on January 9-10.
Infantino, who had until now proposed a 48-team event but with a traditional 32 countries advancing to the finals, will submit his latest proposal at a FIFA Council meeting in Zurich on January 9-10.
A letter outlining the new format was due to be sent to the members of the FIFA Council on Wednesday, the source said, adding that the format was "preferred by president Infantino."
Under the new format, the source said, "every qualified team would play at least two group matches. The top two in each group would then go through to the last 32."
The FIFA Council will vote on several proposals at their January meeting: whether to maintain the current World Cup format of 32 teams, extend it to 40 teams or go to 48 teams.
In the latter case they will vote on whether to have an initial play-off before 32 teams go into a group stage, or whether to go with Infantino's now preferred option.
The successor to the disgraced Sepp Blatter had previously floated the idea of having 32 teams going into a play-off round, with the 16 winners joining another 16 sides in the group stage.
The play-off matches would be staged in the country hosting the finals, but would mean the losers go home after just one game.
"This way, every team is guaranteed at least two matches and then we have knockout matches from the last 32," the source added of the 16-group proposal.
"Furthermore, this formula offers two advantages. Each confederation has a guaranteed number of qualified teams and it is easier to understand for spectators, television companies and sponsors."
The source added that this format "seems to be liked" by the different federations.
The proposal to change the format of the competition is driven by a desire to increase income from marketing and television rights, even if the costs would also increase with an expanded tournament.
Infantino, formerly Michel Platini's right-hand man at UEFA, said recently he was in favour of a World Cup jointly organised by several countries to share out the burden of providing facilities for the tournament.
"We don't want white elephants," he said in reference to stadiums that have been built for past World Cups and then left without a purpose after the tournament. "We want facilities that will last."
Infantino was general secretary of UEFA when European football's governing body expanded the European Championship from 16 teams to 24 for this year's finals in France.
They also approved staging Euro 2020 in 13 different countries around the continent.
And the Swiss-Italian has also been looking to expand the FIFA Club World Cup from the current seven-team format to a 32-club competition and hosting it in June instead of December.
This year's competition in Japan begins on Thursday, with Real Madrid the favourites.