The 28-year-old has encountered a disappointing return to the Blues this season after becoming the club's transfer record signing last summer.
Lukaku signed for Chelsea from Inter Milan for £97.8 million but has only managed five goals in 23 Premier League appearances.
He recently lost his place in Thomas Tuchel's starting XI to Kai Havertz, with the German being deployed as a false 9.
Lukaku and Tuchel's relationship has been strained since the striker spoke of his frustrations with his manager's system in an interview with Sky Italia.
He has since apologized but his time at the club has ever since been plagued with the feeling of a fractious relationship between himself and Tuchel.
According to the Evening Standard, he will reject any interest from AC Milan or Newcastle United even as he continues to fall out of favor with Thomas Tuchel.
His astronomical wages of £300,000-a-week are likely to deter a host of top European sides, including his former side Inter Milan.
Newcastle, with their new-found riches, are viewed as one of the few clubs that will be able to meet Lukaku's demands. However, as the aforementioned source reports, the Belgian himself would not consider a move to the Magpies.
When Lukaku spoke to Sky Italia last year, he highlighted his regret at the way he left Inter Milan and said that wanted to return one day.
But the Daily Star reports that if the striker wants to return to the Serie A side this summer, he would have to half his wages.
Chelsea striker Romelu Lukaku's frustrations growing at Stamford Bridge
To say Romelu Lukaku has been disappointing this campaign would be an understatement.
The 28-year-old arrived at Chelsea with a reputation for being one of the top strikers in European football, having been vital in Inter's Serie A win of 2021.
"They are going to be serious this season. They were last season but they’re going to be really serious in terms of the Premier League."
"He will go into that Chelsea team and make them real challengers for the Premier League title."
The polar opposite has occurred for Lukaku as he has failed to find form and is now growing more and more frustrated with his situation.
Thomas Tuchel did not to even bring him on as a substitute during his side's 1-0 loss to Everton on May 1.