According to letters seen by The Daily Telegraph, the SFO said it was pursuing "every reasonable line of inquiry" to decide whether it can open an investigation into the allegations of unlawful conduct during the bidding process for the 2018 and 2022 tournaments.
Fifa, which faced worldwide criticism for its handling of an inquiry into the bids, last week announced it has lodged a criminal complaint with the Swiss attorney general regarding "possible misconduct of individual persons" in connection with the bids.
Regarding the potential for a Serious Fraud Office inquiry, a spokesperson confirmed to ITV News:
There is no information which has so far been brought to the SFO’s attention that shows that the UK criminal courts would accept jurisdiction. We continue to monitor the situation and to keep the jurisdictional position under review.
– Serious Fraud Office spokesperson