Burnley caretaker manager Craig Bellamy is in the frame for the Wales job.
Wales are seeking a new coach after the dismissal of Rob Page on Friday.
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The Guardian says Bellamy could leave Burnley for the Wales post.
However, the FA is in no hurry because the next match is not played until September.
Manchester United great Ryan Giggs, who previously served as Wales captain, is also said to be interested in returning to his former role.