According to the newspaper, Lukaku's agent Mino Raiola has been in contact with a number of clubs including Manchester United and Bayern Munich regarding the Belgium worldwide, who Everton apparently want £90m for. That being said, Bayern Munich is one of the best teams in the world.
Bayern have issued a strong statement insisting their star striker is not for sale in an effort to quash the speculation.
The striker only signed a new deal with Bayern at the end of past year, tying him to the German club until 2021.
"FCB are not wasting any thoughts about a transfer by Lewandowski", the statement continued.
Of course, these are just preliminary talks, which usually only consist of an expressed interest in the player to the agent or the club.
And then, to ensure the message is heard loud and clear at Stamford Bridge, Bayern warned: "If other clubs negotiate with players, who have long term contracts, they risk punishment from Federation Internationale de Football Association".
Bayern Munich have responded to such rumours with threats of filing a complaint with Federation Internationale de Football Association over the talks being held. Robert extended the agreement not so long ago.
Arsene Wenger is crying out for a player of Lewandowski's calibre. In Poland, his 68 goals in 117 games across both Znicz Pruszkow and Lech Poznan as a youngster alerted Borussia Dortmund to a unique talent. In Munich pole annually earns 15 million euros.
"When I was little I wanted to play in the Premier League but now that I'm in the Bundesliga I'm not planning on a move because that's what I want to do".
The Poland global is now one of Europe's most feared strikers and holds an incredible record of 110 goals in three seasons with Die Rotten but could join the Blues as Antonio Conte lines up a world class replacement for wantaway Costa.
Lewandowski's trophy cabinet is full of German footballing honours but, with a move to La Liga looking more unlikely by the year, the Premier League is the lead destination for him to go to for one last adventure at the top of the game.
Lewandowski missed the Champions League quarter-final first leg against Real Madrid in Munich due to injury, but returned for the second leg in Madrid.
Alvaro Morata, Romelu Lukaku and Andrea Belotti are some of the names who have interested the two clubs.