Charged with rebellion, sedition and misuse of public funds, Puigdemont faces arrest if he returns to Spain over his role in Catalonia's independence drive. He has been living in Belgium in self-imposed exile since the end of October.
Asked about the possibility of Puigdemont entering Spain incognito, Interior Minister Juan Ignacio Zoido told the TVE television channel: "We are taking steps along the border and inside the country, everywhere, to see that that does not happen.
"We are doing it in such a way that he cannot enter (the Catalan parliament) even in the boot of a car."
Zoido said he was "very worried as one cannot tell what someone like him can do."
Puigdemont on Monday vowed to form a new government after the speaker of the Catalan parliament proposed him as president of Catalonia following a snap election in December in which separatist parties once again won an absolute majority.
Zoido said police and the paramilitary Guardia Civil were working "morning, noon and night" to prevent Puigdemont's return.
Accusing the fugitive leader of staging a "circus", Zoido said: "He is fleeing Spanish justice and it cannot be he who determines the sequence of events."
Puigdemont wants to be sworn in from Belgium but Zoido said legal experts in the Catalan parliament had said "an investiture involving video link is not possible."
The government in Madrid has ruled out his being allowed to rule from outside the country and even his separatist allies -- the leftwing ERC party of Puigdemont's former deputy Oriol Junqueras -- are cool in private towards his bid to rule from abroad.