Sánchez has offered political dialogue - welcomed by new Catalan leader Quim Torra - but has also insisted on the inviolability of the constitution, which underlines the "indissoluble unity of the Spanish nation".
Nevertheless, Catalan leaders have made clear their demands on a number of key issues.
Ernest Maragall, the new Catalan secretary for external affairs, told local radio that the "first measure" should be "the freedom of the political prisoners and the return of those in exile".
On Thursday, the Spanish Supreme Court court will study appeals from 14 Catalan politicians charged with rebellion, providing an opportunity for state prosecutors to soften their stance.
But ultimately, the cases are in the hands of Judge Pablo Llarena, and few believe that a sudden about turn is a genuine possibility.
Sánchez's policy on Catalonia has shifted back and forth over the years, but he has eyed a wholesale reform of the relationship between the state and Spain's 17 autonomous communities.
The PSOE has also alluded to revisiting the thorny issue of Catalonia's Statute of Autonomy, the 2010 gutting of which by Spain's Constitutional Court - on petition from Rajoy's party - is widely regarded as the catalyst for the Catalan independence drive.
But the fragility of Sánchez's minority Government, as well as opposition from PSOE grandees to concessions on Catalonia, is an obstacle to movement on either.
Lola Garcia, associate director of the Barcelona-based daily La Vanguardia, wrote that the new Prime Minister's approach to the eternally corrosive issue of Catalonia was that of one "who finds himself in a minefield".