The centre-back has been tipped to return to Camp Nou, where he was a youth player until 2017, since telling Manchester City last year he would not be signing a new contract.
It has been suggested Barca could look to bring in Garcia this month to bolster their defence, but Freixa suggested January incomings are highly unlikely due to their financial problems.
Instead, the 20-year-old Spain international is expected to join after his contract expires this year.
Speaking after a meeting with the interim Barca board and other presidential candidates, Freixa was quoted by Sport as saying: "We've valued the signing of Eric Garcia, but he will arrive in the summer when the season ends and he's available for free."
Freixa, who is running for president against favourite Joan Laporta and Victor Font, says head coach Ronald Koeman has not made any demands for the present transfer window.
Indeed, spending is highly unlikely given the major impact of the coronavirus pandemic on the club's finances.
Barca posted pre-tax losses of €100million last season, with debt more than doubling to €488m, as a 24-per-cent reduction in matchday revenues and a drop in merchandise sales took a huge toll.
The senior players agreed to a wage cut to help reduce costs and prevent club staff being made redundant, which helped to save €74m, but investment in the squad this year remains difficult.
"Koeman has not demanded anything," said Freixa. "He's only stated what is needed. We talked about what to do, and in the current situation, we cannot spend.
"The situation of the club is what it is. What we all know is that it's a critical situation as a result of the stadium being closed and we can't generate income as we normally did.
"But it's not an alarming situation that requires us to take an extraordinary decision."
Freixa added that the elections are due to be held on March 7, having been postponed this month to avoid the risk of members travelling to polling stations amid rising coronavirus cases across Spain.
"They've explained to us that the implementation of postal voting won't allow for the voting date to be earlier than March 7. Therefore, it's set for that date," he said.