The Colombia International has been interesting, some of the largest clubs in Europe, including Barcelona and Atletico Madrid.
However, Corriere di Bologna reports that Bournemouth was first introduced this week with an offer for Lucumi.
The cherries have submitted an offer of € 15 million for the defender, who was immediately rejected.
Bologna is selling at least € 20 million to sell Lucumi, where Roma also keeps a close eye on developments.