It comes after bank accounts at Barclays, HSBC and Standard Chartered Bank were allegedly used to transfer cash as part of the conspiracy.
The three British-based international banks were named on the indictment released by the US Department of Justice, which charged a total of 18 people over alleged bribes inside Fifa totalling more than $150m (£98m) for television rights, sponsorship deals and World Cup votes.
A spokeswoman for the Serious Fraud Office (SFO) in London said: “The SFO continues actively to assess material in its possession and has made plain that it stands ready to assist ongoing international criminal investigations.”
The SFO would not comment on what the material is or when it first came to its attention.
On Friday, Prime Minister David Cameron urged under-fire Fifa president Sepp Blatter to step aside, saying “the sooner that happens the better”.
Speaking in Berlin about Mr Blatter, the PM said: “In my view he should go. You cannot have accusations of corruption at this level and on this scale in this organisation and pretend that the person currently leading it is the right person to take it forward. That cannot be the case.
“Frankly what we have seen is the ugly side of the beautiful game and he should go.
“And the sooner that happens the better and the faster that organisation can start to rebuild its credibility which is so important because so many people around the world want to see this game properly managed, properly looked after so we can all enjoy the World Cups of the future.”