The 31-year-old is out of contract at the Hawthorns this summer and therefore free to negotiate directly with overseas clubs having entered the final six months of his deal.
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David Beckham's franchise Inter Miami made a contract offer during the January transfer window but that proposal was rejected with sources telling ESPN it represented a fraction of his 70,000-a-week wage.
Gibbs is the highest-paid player at West Brom, who have no plans to renew his contract and will need to slash their wage bill should they be relegated from the Premier League. Sam Allardyce's side are in 19th place -- 11 points from safety.
Gibbs' willingness to consider moving to Miami has alerted other MLS clubs with the Red Bulls contacting Gibbs' representatives to explore the possibility of reaching an agreement.
DC United are in the market to sign a left-back during the close season and are also thought to have made a tentative enquiry.
Sources close to negotiations told ESPN Miami remain the front-runners with talks ongoing but no deal is imminent at this stage.
Gibbs has made 100 appearances for West Brom since joining in 2017 from Arsenal, where he won two FA Cups and two Community Shields after coming through the Gunners' youth ranks.
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