Barca coach Ronald Koeman was also hopeful of signing another forward in January, with Lyon's Memphis Depay a target, but will have to work with the players he already has between now and the end of the season.
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Barca were due to elect a new president on Jan. 24 after Josep Maria Bartomeu resigned in October following a movement to have him face a vote of no confidence.
However, following a meeting on Friday, it was decided in conjunction with the local government that it would be irresponsible to hold the election next week due to the rising number of COVID-19 cases in Catalonia.
Acting president Carles Tusquets met with the three candidates for the presidency -- Joan Laporta, Victor Font and Toni Freixa -- later on Friday to discuss a new date.
March 7 was agreed upon, which means Barca will remain without a president through the January transfer window.
Tusquets does not have the power to make signings but sporting director Ramon Planes, with the backing of Koeman, has been working on deals for the incoming president to sign off.
A loose agreement is in place to sign Manchester City defender Garcia, who is out of contract in the summer, for a fee of around €6 million but the three candidates refused to sanction the signing.
"[Tusquets] informed us that there's a possibility to sign Eric Garcia," Laporta confirmed to reporters after Friday's meeting.
"But he is out of contract in June and would be available on a free transfer -- as long as the sporting structure in place at that time green light the signing.
"The club informed us there is no money; that they have to look for imaginative ways to be able to pay [City]. So, we must see in June, when there is no transfer cost involved."
With Gerard Pique out with a knee injury for the foreseeable future, Koeman had been keen to bring in another centre-back this month after failing to land Garcia, who left Barca for City in 2017, last summer.
The Dutch coach has also been open about his desire to sign Depay from Lyon, another player who is available for free at the end of the season.