Appearing at a government coronavirus briefing on Sunday, Illa spoke about the prospect of LaLiga returning.
There have been no Spanish top-flight games since early March, and although there are hopes matches could start from June, Illa was careful not to present any timeframe.
He said: “I cannot say if football is going to be able to restart its activity before summer. It would be imprudent of me to offer a definitive view.”
LaLiga teams have been given the go-ahead to return to training, possibly as soon as early May, providing they abide by Spanish government protocols.
That decision was reached in a meeting last weekend between Spain’s National Sports Council (CSD), the Royal Spanish Football Federation (RFEF) and LaLiga.
However, staging games is clearly some way off, and it seems certain any resumption would mean fixtures being played initially behind closed doors.
Reports have suggested clubs and league officials could be targeting a return to action on June 6 or June 13; however, Illa’s circumspection indicates Spain’s reluctance to rush into any such decision.
Barcelona head the league table after 27 rounds of the 38-game season, two points clear of nearest rivals Real Madrid.
Spain has been severely hit by the pandemic, with the country suffering over 23,000 deaths.