The couple have been dating since 2010; a royal court spokesperson confirmed the romance in August of that year after months of speculation.
An engagement would coincide with another happy royal event, the birth of Princess Madeleine's first baby. The little girl is due in February, eight months after Madeleine's wedding to financier Christopher O'Neill, with a christening to follow a few months later.
As the older brother of Madeleine, 34-year-old Carl is said to be keen to start a family of his own – his sister Crown Princess Victoria is also a mother to Princess Estelle, who will be two in February.
There has been no word from the Royal Household on the engagement reports. But it would come as no surprise to royal watchers.
The Prince and Sofia have been living together in Djurgården, an affluent neighbourhood in Stockholm, for some time now, and it's clear that King Carl XVI Gustaf and Queen Silvia of Sweden have warmly accepted their son's girlfriend, who spent New Year with the royal family in the Swiss Alps.
The Swedish media are speculating that an engagement announcement will be made any day now, giving the country another wedding celebration to look forward to.