Sam Allardyce has said that England are being held back by the Premier League ahead of his expected appointment this week.
Coleman guided Wales to the Euro 2016 semifinals, where they were beaten 2-0 by Portugal.
The FA wants to hold talks with Arsene Wenger to find out whether he is interested in taking over as England coach, the Telegraph reports.
Guus Hiddink has put himself forward as a surprise candidate to succeed Roy Hodgson as England manager, according to The Times.
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Coleman, who succeeded the late Gary Speed in January 2012, guided Wales to Euro 2016 qualification.