The 71-year-old Aragones, who led Spain to victory at Euro 2008 and had a spell as Sevilla coach in the mid-1990s, had lunch with Del Nido in Cordoba to discuss taking over from Manolo Jimenez, who was sacked after Tuesday's 1-1 draw with Xerez.
"If I have come to Cordoba it's because I am interested in Luis, but we'll both now think it over," Del Nido was quoted as saying by As newspaper. "We have given ourselves 24 hours."
The club could not immediately be reached for comment.
Aragones, out of work after leaving Turkish club Fenerbahce at the end of last season, told As he was excited about the idea of coaching again and the paper reported he was pushing for a contract through to the end of next season.
In a coaching career stretching back to 1974, he has taken the helm at Atletico Madrid, Barcelona, Espanyol, Real Betis, Valencia, Real Oviedo and Real Mallorca.
Nicknamed the "wise man of Hortaleza", after the Madrid neighbourhood he grew up in, Aragones also played for Atletico, whom Sevilla will face in the King's Cup final in May.
Sevilla suffered a surprise Champions League exit to CSKA Moscow last week and Tuesday's draw with Xerez, who are bottom of the table, meant the Andalusian club had failed to win in seven matches in all competitions.
The club are fifth in La Liga on 45 points, one behind Real Mallorca, who occupy Spain's fourth Champions League qualification spot.
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