The Cherries have concerns over defender Marcos Senesi with his contract running down this season.
The Argentina international is interesting Barcelona, where sports director Deco has had him scouted this term.
As such, Bournemouth are preparing to replace Senesi and have Muharemovic on their shortlist.
Sky Italia's Gianluca di Marzio is reporting Bournemouth have joined Inter Milan in expressing interest in Muharemovic in recent days.