The Association will have on their list of targets to replace when the manager leaves his current role.
Southgate is under contract with the FA until the end of 2024, although the report that there is every chance he will leave after the European Championships next year.
The report states that the FA are already eyeing up potential successors and the Manchester City manager is obviously an excellent candidate for any managerial role.
There are obvious problems for the FA in any pursuit of Guardiola, firstly in tempting him into an international position, a role the 52-year-old has never held.
Guardiola is also under contract at Manchester City until 2025 so for him to replace Southgate either after the Euros or at the end of 2024 would see him leaving the Premier League champions before the end of that deal.
That would not only be extremely expensive for the FA, but seems unlikely that Guardiola would depart without seeing out that contract, with leaving in the middle of a season almost unthinkable.
Much could change by the end of the European Championships and it is not guaranteed that Southgate will leave after that tournament, or even at the end of 2024.
Other candidates will also be in the running as and when Southgate does depart, with the likes of Newcastle manager Eddie Howe and Nottingham Forest boss Steve Cooper likely to be in contention.
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