Mikel, 33, is currently without a club having left Turkish Super Lig outfit Trabzonspor by mutual consent in March.
The Baggies are currently second in the Sky Bet Championship and look well placed to secure a return to the Premier League following a two-season absence from the top flight.
Mikel enjoyed a successful spell at Chelsea earlier in his career, winning multiple titles.
He had a brief spell with Middlesbrough in the Championship during the 2018/19 campaign, featuring 19 times, scoring once.
The former Lyn Oslo of Norway player has also been linked with Brazilian clubs Botafogo and Internacional as well as Serie A newcomers Benevento.
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