With his €28m buyout clause having just expired, new Sunderland football chief Florent Ghisofli is aiming to strike terms with Bologna for €20-25m.
TMW says Bologna are reluctant to sell, particularly as they're about to lose fellow centre-half Sam Beukema to Napoli.
Instead, Bologna intend to trigger a 12-month option in Lucumi's deal to extend it to 2027.
Bologna also wish to raise his salary beyond the current €1m-a-year terms. However, Lucumi is stalling on negotiations after learning of Sunderland's interest.
"We've already spoken with him and are willing to extend his contract. We'll meet with him and his agent in the coming days," said Bologna chief Claudio Fenucci last week.