The outlet claims that both the Hammers and their Premier League rivals Everton have contacted the Scot, having both held crisis talks about their current managers.
Manuel Pellegrini and Marco Silva are both under huge pressure amid alarming slumps in form, which is why perennial fixer Moyes has emerged as a candidate for both jobs.
The 56-year-old is eager to return to management, but would prefer a return to the Toffees than a London Stadium reunion. The Irons want a manager with top flight experience if they were to sack Pellegrini.
This isn’t a potential appointment that is likely to excite many West Ham fans. Moyes did a pretty good job when he was in charge previously, rescuing Slaven Bilic’s mess and steering the club away from relegation danger. However, he was then given the boot rather unceremoniously in favour of the high-profile Pellegrini. Clearly that hasn’t quite worked out, as we are seeing at the moment. Neither did Bilic when he replaced Sam Allardyce, a similarly flashy appointment after the hardened Premier League substance of a Moyes-Allardyce type. It seems that David Gold and David Sullivan have come full circle, and are now so desperate to see results improve that they are begging Moyes to come back. Unfortunately for them, though, Everton are also an absolute shambles and are looking in the same direction as they are. Understandably, Moyes would prefer a Goodison Park return. Where that would leave West Ham remains to be seen. Big Sam, anyone?