A number of players are weighing up their futures at the club ahead of the summer transfer window, according to reports.
New Blues owner Todd Boehly has completed his takeover at Stamford Bridge and the consortium led by the American billionaire are expected to invest in the squad.
Meanwhile, there are imminent player exits already, with Antonio Rudiger and Andreas Christensen leaving the club when their contracts expire at the end of June.
£97.5million summer signing has also been linked with an exit from Stamford Bridge, less than a year after re-joining the club.
The 29-year-old has endured a frustrating return to Chelsea, struggling to recapture the excellent form he displayed at previous club Inter Milan.
report that Lukaku and fellow forwards Timo Werner, Hakim Ziyech and Christian Pulisic are all considering where their futures lie.
Thomas Tuchel has been able to field a number of attacking options across his front three this year, meaning some have had to settle for a lack of playing time.
One of the players mentioned in the report, Pulisic, has already fielded questions on his plans.
When the winger, who is on international duty with the USA, was asked whether he sees his future at Chelsea, he said: ‘As far as right now, I’m obviously just focused on what I’m doing here. And I’m super excited to be here. And yeah, that’s it.
‘Of course, I want to get more playing time. I want to be on the field as much as I can and be the sharpest I can be and fit as well.
‘I think I still got a lot of games, but it’s always something that I’m working at and trying to be regular at club level as well to put myself in the best position to be fit when I come here with the national team.’
Pulisic did also say, however, that he is ‘excited’ about the future after meeting Chelsea’s new owners.
‘At the end of the season, we were able to meet with them and they were around the club a lot,’ Pulisic added.
‘They are really good people so I’m excited moving forward.’
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