Bournemouth have been relegated from the Premier League, and the Cherries are likely to sell some of their best players.
The report in the British tabloid added that the 28-year-old himself is looking to leave Bournemouth.
The Telegraph has now claimed that Newcastle are interested in King as well, and that the Magpies are also looking to sign his Bournemouth teammate and midfielder David Brooks.
King made 24 starts and two substitute appearances in the Premier League for Bournemouth this past season, scoring six goals and providing four assists in the process, according to WhoScored.
The Norway international made 34 starts and one substitute appearance in the league for the Cherries in 2018-19, scoring 12 goals and providing three assists in the process, according to WhoScored.
Everton or Newcastle United?
While Newcastle are a big club, Everton are more ambitious, and under Carlo Ancelotti, the Merseyside outfit are likely to challenge for the European places next season.
A move to Everton would make sense for Norway international forward King.