Bale's time at Real Madrid will officially come to an end on June 30, and the 32-year-old has agreed a deal to join Los Angeles as a free agent.
The former Tottenham Hotspur man confirmed his imminent arrival in the States on his social media accounts as he aims to keep his fitness up before the 2022 World Cup.
Bale was linked with switches to Getafe and Cardiff City before sealing a deal with Los Angeles, and Thorrington is optimistic that player and club can have a successful "long-term partnership".
"I'd love to get into specifics but I don't as a policy, but what I can tell you is that LAFC and Gareth are hoping that this is a long-term partnership," Thorrington told a press conference.
"It was never about six months just for the World Cup. We were always talking about longer term than that. That was very clear from Gareth and his representative.
"When Gareth is looking at what he needs to do, his priority will be at LAFC - we are absolutely sure of that - but we're not naive to the fact that he, like some other players of ours, have a World Cup on the horizon."
The LAFC chief also affirmed that a date for Bale's official transfer had not been pencilled in, but the club are hopeful of dotting the i's and crossing the t's within the next 10 days.
"We don't have a firm date. Our transfer window opens in early July when we can register [players]. We still have to go through paperwork, hopefully a week or the next 10 days to take care of that, to welcome him and his family to LA, get up to speed," Thorrington added.
"It wasn't a financial conversation with Gareth or us. If Gareth was making this decision with financial motives he wouldn't be in MLS.
"This league is really exciting globally and he saw an opportunity to make a real impact. He sees here an opportunity to make a difference with the stage we provide.
"His priority will be at LAFC but we're not naive - he has a World Cup on the horizon and how we manage his preparation ahead of the World Cup will be important to Gareth and the success of LA, but we want him peaking after the game with the US!"
Bale will follow Giorgio Chiellini to Los Angeles after the Euro 2020 winner agreed a deal to sign for the MLS side from Juventus, and he departs Real Madrid after a trophy-laden but controversial nine-year spell.
The Wales international won five Champions League titles with Los Blancos, as well as three La Liga titles, four Club World Cups, one Copa del Rey, three UEFA Super Cups and three Supercopa de Espana crowns.
Bale amassed 106 goals and 67 assists from 256 appearances for the Bernabeu outfit in all competitions, but he only made seven appearances in the 2021-22 season amid injuries and rife competition for attacking spots.
Los Angeles will take on LA Galaxy in a July 9 derby, and Bale could potentially make his debut for the MLS outfit in that match once his departure from Real Madrid is confirmed.
The ex-Southampton youngster will lead Wales into their first World Cup since 1958 this winter, with Iran, England and the USA awaiting Rob Page's side in Group B.