Mikel, 33, is currently without a club having left Turkish Super Lig outfit Trabzonspor by mutual consent in March.
The midfielder has also been linked with Championship promotion hopefuls West Brom.
However, there is also contact with the Hammers and talks are underway about next season.
Ultimately, Mikel’s final decision will depend on whether the team in question is in the Premier League next season.
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.