The 19-year-old suffered a serious knee injury during Spain's Euro 2024 qualification match with Georgia last month, with the damage occurring when he twisted in an attempt to control the ball.
Scans revealed that the midfielder had completely torn his ACL, in addition to damaging his lateral meniscus, and he will be missing for the remainder of the 2023-24 campaign.
The club are able to use 80% of the Spaniard's salary due to the length of his absence, and Laporta has said that the plan is to loan a midfielder for the second half of the campaign.
"If we manage to have a fair play, the idea is to have a midfielder who somehow compensates for Gavi's loss. It would be a transfer until the end of the season, as we did many years ago with Edgar Davids, for example," Laporta told Mundo Deportivo.
"We have a margin, I think that until the end of the year we can generate 'fair play', for a series of operations that we have underway and if they are confirmed, we would have options."
Laporta also confirmed that Vitor Roque is set to arrive in January, with Gavi's injury not impacting the club's plans for the 18-year-old, who has agreed to join from Athletico Paranaense.
"He is scheduled to arrive at the end of December or the beginning of January, for this winter market. The idea is that he will be incorporated as soon as possible," said the president.
"Deco explained to us that he is a player who has a 'goal' in him and I think now we will do very well, because he can help us a lot. We have virtuous players, natural scorers like [Robert] Lewandowski and Roque will complement the team."
Roque has represented his current side on 81 occasions in all competitions, scoring 28 goals and registering 11 assists in the process.
Laporta also commented on his side's plans for the summer transfer window, including potential permanent moves for Joao Felix and Joao Cancelo, who are on loan from Atletico Madrid and Manchester City respectively.
"If we meet the budget, which is very ambitious, we could go to the market with the guarantees of doing operations that do not involve personal guarantees of the board and it would be a matter of being able to sign normally," he said.
"The agent of the players (Jorge Medes) is the same, and the two clubs - Manchester City and Atletico Madrid - with which we have a good relationship and we know each other a lot, have already guided us.
"We are interested in both players not being on loan, but joining us permanently. Let's see how it evolves. I think both, the Cancelo and Felix operations that will satisfy all parties."
Barcelona will be bidding to return to winning ways in Spain's top flight when they take on basement side Almeria in their final match of 2023 on Wednesday night.