The Everton star has recently followed Blues stars N’Golo Kante and Gary Cahill, as well as youngster Lewis Baker.
It could be a big hint that he may be preparing for a move back to Stamford Bridge.
Manchester United are desperate to sign Lukaku as they want a big No.9 to lead their attack.
But it was claimed by Italian journalist Tancredi Palmeri that an agreement in principle with Chelsea had already been done.
Palmeri is a renowned transfer guru who has worked for a variety of media outlets.
He tweeted: “Chelsea have reached an agreement on principles with Lukaku. Still under negotiations the fee with Everton.”
Romelu Lukaku may have dropped a Twitter transfer hint Romelu Lukaku transfer odds: Where next for the Everton star? Tue, June 6, 2017
Where could Everton ace Romelu Lukaku go next, according to Skybet odds?
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Arsenal – 33/1
Palmeri was subsequently asked if Chelsea would pay £100m to bring Lukaku back to Stamford Bridge.
He replied: “Don't think so. Doesn't look like an easy negotiation. Lukaku though could force it.”
Lukaku joined Chelsea as an 18-year-old in 2011 after making the move from Anderlecht for £10m.
He is represented by Mino Raiola, the man who did a world-record deal to take Paul Pogba to United last summer.
The Belgian striker seems to have made a decision on his future – although he is yet to reveal it publicly.
"My agent knows what's going to happen," the 24-year-old told Sky Sports.
Romelu Lukaku joined Chelsea as an 18-year-old in 2011
"I know what I want to do, and whenever some"
According to the Independent, United made an enquiry over the possibility of signing the Belgian, and while they were not given a firm “no”, the Old Trafford club were told that a deal with Chelsea is very close.
They add a move for the talented striker is expected to cost upwards of £80m.
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Lukaku's current wages of £80,000 a week are also set to be doubled when he completes his return to Stamford Bridge.
The 24-year-old was at Chelsea between 2011 and 2014 but failed to be given the chance to impress before he was sold to Everton by Jose Mourinho in 2014.