An independent commission has still not published its ruling, more than a year and a half after the disciplinary hearing concluded and three and a half years since Manchester City were first charged. City have consistently denied any wrongdoing throughout the process.
Asked whether the length of the process was a source of frustration for Arsenal, Garlick told BBC Sport: "It has gone on for a while. Everybody – the league and the teams – would want the clarity around what's going to happen next. But it's not something that I can control.
"It's not something that I can speculate on. And I just hope that there is a solution very quickly."
Garlick's comments arrived on the eve of the new season, shortly after Premier League chief executive Richard Masters said: "I do accept it's taking longer than expected, and I understand that people want to find out as soon as possible what's going on, but I simply can't provide that."
Describing the case as "hugely complex," Masters added that the league's rules require the independent process to run its course before any outcome can be confirmed.
Privately, officials at several other Premier League clubs have also voiced frustration over the delay in recent conversations with BBC Sport, while acknowledging that the commission is operating on its own independent timetable.
One club official suggested the league should be "actively seeking to put in place a better system" to secure faster resolutions in future, while another pointed to the £45m the league spent on legal costs during the 2023-24 season alone as evidence of the spiralling expense of such a prolonged dispute.
The charges City are contesting relate to alleged failures to provide accurate financial information between the 2009-10 and 2017-18 seasons, alleged breaches of Uefa's financial fair play rules between 2013-14 and 2017-18, and alleged breaches of the Premier League's own profitability and sustainability rules between 2015-16 and 2017-18. City also face separate charges of failing to co-operate with the league's investigation between December 2018 and February 2023.
Arsenal finished as Premier League runners-up to City in both 2023 and 2024, on the latter occasion by just two points. Along with Liverpool, Manchester United and Tottenham, the club reportedly served legal notices on City in 2024 reserving the right to seek compensation should the club be found guilty, with some estimates of potential losses running above £100m.
Those clubs may have taken encouragement from Everton being ordered in June to pay Burnley £35m in compensation over the impact of a separate breach of the league's financial rules.