Laporta firstly denied that Lionel Messi would ever leave amidst rumours the Argentine could be tempted by a move away from the Catalan side, but admitted their young Brazil international may have to depart.
United held talks with Barca over a potential move during the summer, something which the player himself admitted. The Champions League holders, though, deemed the Red Devils' bid unacceptable.
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Now, however, it appears the club might be forced into selling the Brazilian. Laporta said, as per the Daily Mail: "For Neymar, it's different.
"The economic situation of the club is not good, but the current president, to balance the books, must sell players or assets. And the best solution is to sell a great player.
"There is talk of a proposal for Man United. But all that, it is because of the mismanagement of the current leadership."
However, just the day before, current president Josep Maria Bartomeu claimed the La Liga champions were planning to offer Neymar a new deal worth £500,000-per-week.
"This is the season we will sort out a new deal with Neymar," Bartomeu said, reported the Mirror.
"But we will try not to talk about the negotiations and to work discreetly until we can announce it."
Tha Brazil captain has stood out for Barcelona this season in the absense star man Messi, who has been sidelined with an injury he picked up in September against Las Palmas.
With eight goals in 11 appearances, it is easy to see why Louis van Gaal's United hope to bring the Ballon d'Or nominee to Old Trafford.
However, despite rumours surrounding Neymar's future and Barcelona's financial struggles, it's difficult to picture either party sanctioning a move.
The Brazilian joined Barcelona from Santos in June 2013 for £49 million and endured an inconsistent first season, but has since gone from strength-to-strength to become a vital cog in Barca's team, helping to secure the league, Champions League and Copa del Rey treble last season.