Puigdemont has been in self-imposed exile in the country since fleeing Spain just days after the Catalan parliament declared independence from Madrid in October.
But after his Together for Catalonia grouping came first in a regional snap election, he was named their candidate to once again rule the region.
His party submitted the proposal to Catalan's parliament, in an attempt to get around Spain's constitutional law, which says a candidate must be present at the regional parliament to be officially appointed.
The proposal, seen by AFP, says the Catalan parliament could "authorize, by an absolute majority, to hold an investiture debate without the presence and intervention of the candidate".
It would also allow for a "remote" government, notably carried out using emails, audio conferences and video conferences.
Spain issued a European arrest warrant against Puigdemont but later dropped it. However, he faces arrest if he returns to Spain for leading the secession bid in the deeply divided northeastern region.
Catalan separatists are divided over how to form an effective regional government. The proposal is reportedly not backed by Catalonia's jailed former vice president Oriol Junqueras, from the Republican Left of Catalonia pro-independence party.
He has instead suggested that Puigdemont could rule as a "symbolic" president with a fully functioning executive on site.