The British tabloid has claimed that the Nigerian has been in London this week in order to negotiate a deal.
The 28-year-old joined Al Ain FC on a season-long loan deal in the summer of 2015, but it has been cut short.
“Fenerbahce want at least £7million for their striker on a permanent deal or thrash out terms for another loan.”
Emenike has played for Karabukspor and Spartak Moscow among other clubs, and it does come as a surprise that West Ham are (reportedly) interested in him.
The Hammers have injury problems at the moment, and perhaps they see the 28-year-old as someone who would be a good addition to the squad in order to boost numbers.
However, it would be best for the London club if they sign Emenike on loan until the end of the season.
That would allow West Ham manager Slaven Bilic to judge whether the Nigerian is good enough for the Premier League.
Spending £7 million on a striker like Emenike who is unlikely to be first choice would not be a good idea.