Barclays and Standard Chartered have launched their own investigations into whether their services were used to pay corrupt Fifa officials.
The UK banks started their internal reviews after football's governing body was plunged into crisis after US authorities charged 14 defendants on Wednesday (27 May) with receiving more than $150m (£100m, €136m) in bribes.
Swiss prosecutors also opened criminal proceedings related to the awarding of the 2018 and 2022 World Cups.
The investigations came as the seemingly beleaguered Sepp Blatter tightened his grip on power at Fifa.
He was elected to a fifth term as president after Prince Ali bin al-Hussein dropped out of the race to succeed him before a second round of voting at Friday's congress vote in Zurich.