Earlier this month the Royal Court announced that the couple had emptied their apartment in New York and were planning to stay in Stockholm for a while, as they discussed where in Europe to be based in the longer term.
According to royal sources speaking to Sweden's Expressen newspaper, the couple have been considering London, Paris and Gstaad in Switzerland, with the British capital now their "top choice".
Chris's mother Eve O'Neil lives in central London, while his sister Tatyana is based on an eighteenth century estate just outside the city.
Expressen wrote on Sunday that the financier also had a "large circle of friends" and "business associates" in the UK.
Others have speculated that Switzerland could be the most likely option for the couple as it is where Chris O'Neil's best man Cedric Notz is based.
But Margareta Thorgren, press spokeswoman for the the Royal Court later told the newspaper "nothing is decided yet. They have taken the decision to move to Europe and then we'll see where things go."
Princess Madeleine revealed the couple's plans to return from the US in the SVT television programme "A year with the royal family 2014", broadcast at the end of last year, saying that she wanted to be closer to her family in Stockholm.
The couple had been living in Manhattan with their baby daughter Leonore and are expecting their second child, who will be sixth in line to the Swedish throne.
Margareta Thorgren refused to respond to questions about why Chris O'Neil could not continue his business – which advises affluent people on how to make financial investments – while living in Stockholm.
"This type of information is not something we can comment on," she said.
Paris is believed to be the least likely option for the couple, although there have been rumours that Chris O'Neil could base himself there during the week, with Princess Madeleine remaining in the Swedish capital.
It is widely expected that the couple will have their next child in Sweden in the summer, with their baby due around the same time as Prince Carl Philip's wedding to former reality television star Sofia Hellqvist.