Leeds are ready to go again in their pursuit of Suzuki now that Meslier's switch to Arsenal has been formally confirmed, though Daniel Farke's side are also weighing up a rival option in Derby County's Zetterstrom.
Meslier has completed a free transfer to Arsenal on a two-year deal, ending a seven-season association with Leeds United that brought 70 clean sheets in 215 appearances and two promotions from the Championship.
"I'm extremely happy. It's a great day for me because I have just joined the champions. For me, Arsenal is the biggest club in England," the 26-year-old said after signing.
His departure, along with the expected exit of Karl Darlow, has left Leeds needing fresh options between the posts. Early exploratory talks over Suzuki failed to produce a breakthrough, with Parma holding out for more than €30m for the 23-year-old, who also has interest from Juventus and other Premier League clubs.
Leeds are not deterred, though, and are ready to return with an improved offer as they look to make the Japan international, who impressed at the World Cup before Japan's exit to Brazil, a priority target.
Zetterstrom, 27, has also emerged as an option after a standout campaign at Derby, where he kept seven clean sheets in 32 Championship appearances and started for Sweden at the World Cup. Leeds and Eintracht Frankfurt have both made contact to enquire about a fee, with Wolves also credited with interest.
Zetterstrom is understood to be keen on a move to Elland Road given the chance to test himself in the Premier League, though Derby - who have him under contract until 2027 - are not in a rush to sell and are braced for offers as the transfer window develops.
Leeds United currently have Lucas Perri and Alex Cairns as their senior goalkeeping options following the departures of Meslier and Darlow, but Perri struggled to hold down the number one spot last season after Darlow was preferred for the closing weeks of the campaign.
Farke is understood to see a new addition between the posts as one of the squad's most pressing needs heading into pre-season, with the club keen to have the situation resolved before the Premier League campaign begins next month.