The Cherries need to rebuild a defence that has lost Dean Huijsen (Real Madrid), Illia Zabarnyi (PSG) and Milos Kerkez (Liverpool).
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And The Sun says Bournemouth are ready to make an offer for Acheampong.
The youngster can play at fullback and centre-half - with Chelsea management rating him highly. As such, the Blues are only interested in sanctioning a straight loan deal.
But Bournemouth want a permanent deal and a source told The Sun: “We have held talks and made our intensions very clear but it's a bit difficult at the moment because Chelsea just want to do a dry loan because obviously they don't want to lose him.
“Hopefully their stance might change in the coming weeks as we get closer to the end of the transfer window.’