De Wever, the Flemish nationalist who emerged as the big winner from Belgium's parliamentary elections last month, ended a mission yesterday on exploring options for a new government.
The end of De Wever's mission paved the way for the king to appoint Di Rupo as prime-minister-in-waiting, with the task of forming a coalition in the next few months.
But the king instead entrusted Di Rupo with "a mission of pre-formation", a new concept which stops short of handing the socialist leader the prime minister's job.
Indeed, it is not yet clear which parties will eventually enter the government, as divisions are still rife between French- and Dutch-speaking parties over the content of the coalition agreement.
There are "convergences between the parties' positions, but not enough to form a government yet," De Wever told Dutch-language broadcaster VRT after meeting the king on Thursday.
Talks are focusing on state reforms which led to the demise of the previous government, namely the redefinition of electoral boundaries around Brussels – which has bilingual status – and the delegation of further powers to the regions, including sensitive talks on social security.
"Elio Di Rupo should try to find common ground between future coalition partners in three main areas: fiscal consolidation, socio-economic issues and state reform. A daunting programme," writes French-language newspaper Le Soir.
De Wever had initially said he hoped a new government could be formed in October, half-way through Belgium's six-month rotating presidency of the EU.
If he eventually becomes prime minister, Di Rupo would be the first French speaker to hold the position since 1974. He would also be the first gay premier in Belgian history.