The former rugby league standout would also appeal to the Rugby Football Union (RFU), who are keen to appoint an Englishman.
"He's committed to us until the World Cup," Gatland told reporters. "But if other opportunities come along, he needs to consider those because he's out of contract after the World Cup.
"There are two or three world-class defensive coaches out there and he's definitely one of them."
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Former Wasps coach Edwards has been part of Gatland's Wales coaching set-up since 2008, the pair winning three Six Nations titles together.
(Reporting by Hardik Vyas in Bengaluru)
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