Labour backbench MP Tom Watson, who has been taking the lead role in exposing corruption in News Corp's UK subsidiary, News International, has written to the SFO, asking it to launch a fresh investigation into alleged criminal activities in the media company.
An SFO spokesperson told Business Standard: "SFO Director Richard Alderman will give full consideration to Watson's letter.
"The SFO is aware that the Metropolitan Police Service is conducting an investigation into alleged improper payments to police officers. The SFO is routinely in contact with the US authorities and will provide assistance as required."
The SFO is an independent government department that investigates and prosecutes serious or complex fraud, and corruption.
It is part of the UK criminal justice system with jurisdiction in England, Wales and Northern Ireland.
The new Bribery Act that came into force in the UK from July 1 is a new anti-corruption law that will be implemented with the SFO as the lead agency.
Meanwhile News International's former CEO, Rebekah Brooks, who was arrested on Sunday, has been let out on bail, taking the total number of arrests in the phone hacking case to 10 so far.
The scandal also saw Metropolitan Police chief Sir Paul Stephenson give his resignation, after it emerged that he had enjoyed free hospitality from a spa resort
alleged to have links to former employees of News International.
Rupert Murdoch's media empire came under further attack over the weekend, with leaders in both the ruling coalition and opposition Labour parties demanding his control over the media (and therefore politics) be re-examined.
Deputy Prime Minister Nick Clegg, leader of the Liberal Democrats party, said the phone hacking allegations against the News of the World (the Sunday tabloid closed as a result of the scandal) had led to "a major crisis in public confidence in yet another pillar of the establishment".
Speaking to the BBC's Andrew Marr this morning, Clegg said the claims showed a "total collapse of decency and values in the way part of the press conduct themselves".
Ed Miliband, leader of the Labour party, told the Observer newspaper, "We've got to look at the situation whereby one person can own more than 20 per cent of the newspaper market, the Sky platform and Sky News.
"That amount of power in one person's hands has clearly led to abuses of power within his organisation. If you want to minimise the abuses of power, then that kind of concentration of power is quite dangerous."
Miliband said that Prime Minister David Cameron was unable to provide the leadership the country needed at the moment.
Cameron is on a two-day trade visit to Africa. It was originally scheduled as a four-day visit.
News Corp chairman Rupert Murdoch, his son, James, and Brooks, his former CEO, are to appear before a Parliamentary committee on Tuesday to give evidence regarding the scandal.