The Serbian forward is keen to rejoin the London club after a successful spell there in the second half of last season, where he scored 12 goals in 20 games, helping the club make their return to the Premier League.
Despite the fact that other Premier League clubs, such as Crystal Palace, are interested in signing the Serbian striker, the Mail's report claims he has made it clear that he wants to return to the Cottagers after his success there.
Mitrovic's national team Serbia have already been knocked out of the World Cup, coming third in Group E, though the striker still managed to get a goal in a 2-1 defeat to Switzerland.
The player moved to Newcastle from Belgian side Anderlecht in 2015 for around £13m, but has since struggled to make a strong impact at the club following various injuries and suspensions.
Fulham are reportedly interested in signing all five of their loan players from last season, including Chelsea's Lucas Piazon and Tomas Kalas, Southampton's Matthew Targett and Brighton's Oliver Norwood.
Newcastle will be hoping to replace Mitrovic with OGC Nice striker Alassane Plea for a reported £27m, as the striker scored 21 goals in Ligue 1 last season and is subsequently wanted by several Premier League clubs, including West Ham and Tottenham Hotspur.