The 22-year-old Ecuador international is one of several options Unai Emery's side are weighing as they look to bolster the position following Ezri Konsa's £55 million move to Arsenal, according to The Athletic's David Ornstein.
No agreement is close on Southampton's Harwood-Bellis, with Aston Villa's opening £18 million bid plus add-ons already rejected by the Saints, who are said to want closer to £25 million.
Ordóñez has established himself as one of Club Brugge's most important players since progressing through the Belgian club's academy, making more than 120 appearances and starting 30 of his 33 league games last season, while winning 141 of 251 contested duels. He extended his contract to 2029 last September, giving Brugge little urgency to sell, and reports in Belgium suggest the gap between the two clubs' valuations remains wide, with Brugge holding out for a fee in the region of £30 million.
Villa's interest in the defender is not new. He has previously been linked with a host of Premier League clubs, including Chelsea, Newcastle and West Ham, while Inter Milan have also registered serious interest, hoping to convince him to move to Italy rather than England.
He's earned 20 caps for Ecuador, including three appearances at this summer's World Cup, and featured ten times in the Champions League last season, experience Villa believe would allow him to adapt quickly to the club's own European commitments.
Villa are working with significant funds following Konsa's departure and remain determined to add fresh defensive cover before the transfer window closes, with the club's interest in Ordóñez confirming their search now extends beyond Harwood-Bellis alone.