Everton manager Ronald Koeman is said to be keen to bring in more firepower this winter, but West Ham are also plotting a bid, the report claims.
Wilson has scored 10 goals in 28 games since Bournemouth's promotion to the Premier League in 2015 and was rewarded with a new contract in the summer.
According to the Daily Mirror, the 24-year-old would cost in excess of £20 million.
Everton missed out on a number of key targets during the summer transfer window and look set to make up for it in January, with negotiations for Manchester United midfielder Morgan Schneiderlin already underway, according to the Telegraph.
West Ham could also be set for a busy winter, with the strikers they signed struggling since moving to England from overseas.
Both Simone Zaza and Jonathan Calleri are already being tipped to depart the London Stadium next month.
Have something to tell us about this article?