Rooney has started only nine Premier League games since Jose Mourinho became United manager in June last year.
His contract runs out in the summer of 2019, but United are expected to allow him to leave at the end of the season.
A senior source at West Ham has confirmed they would be one of the clubs who would try to sign Rooney – if United give any indication that they will let him go.
When asked to comment on how likely it was that Rooney would become a West Ham player, the source said: “Never say never”.
Last month, Mourinho refused to rule out the prospect of Rooney leaving before the Chinese transfer window closed on February 28.
Three Chinese clubs had been interested in signing him – Guangzhou Evergrande, Beijing Guoan and Jiangsu Suning – but on February 23 Rooney released a statement saying he wanted to stay at United.
United signed Rooney from Everton for £27m in 2004. Since then he has won five Premier League titles and the Champions League in 2008.