The 19-year-old moved to the San Siro from Caen last summer on a two-year loan deal.
As part of that agreement, the France under-21 international will join Inter permanently in June 2019 for around £5 million.
However, Karamoh has endured a mixed first season in Italy and it has been claimed he is assessing his future.
As a result, Inter are reportedly in talks with Caen about buying the winger outright now – instead of in 2019 – and then selling him on for a quick profit.
That news has alerted West Ham, who were one of several Premier League sides tracking Karamoh last year.