The Real Madrid midfielder posted a picture of himself outside Hamleys toy shop yesterday.
The Sun subsequently picked up the image and suggested it fuelled speculation he could be on his way to Stamford Bridge.
A day earlier Kroos spent the day at Winter Wonderland in Hyde Park with his son.
But it is far from uncommon for La Liga players to enjoy Christmas outside of Spain.
The league is currently on a winter break – a luxury Premier League stars don’t enjoy – and Real aren’t in action again until January 4.
Hours after publishing, The Sun’s report was no longer available to view on their website.
Links between Kroos and Chelsea are far from new, though.
Back in 2014, when Kroos left Bayern Munich for Real, the German revealed he was open to a move to Stamford Bridge.
He said: “I’m happy to have been given the chance to try something new. Even though it’s only been a short while I feel like it was the right decision.
“Madrid is a special club and the challenge I was looking for after my long and successful career at Bayern.
“Madrid, Bayern, Barcelona and Chelsea are the four biggest clubs at the moment, so I would only have swapped one for another.”
Manchester United were in for him too two years ago and David Moyes last week claimed he had struck a deal for the midfielder.
“Toni Kroos was agreed to come in the summer,” the now Sunderland boss said.
“I had agreed it with Toni himself and his agent.”