Should he be given the green light, the 24-year-old striker will join the Cherries as a free agent.
The Senegal-born frontman has already penned a two-year contract with the Championship new boys, tying him to the club until 2015.
Coulibaly has spent the past four years in Swiss football with Grasshopper, while he has also turned out in France.
He linked up with Bournemouth last week on an initial trial basis and featured in a 2-0 friendly defeat to FC Zurich.
He has done enough to convince Eddie Howe that he is deserving of a permanent stay and becomes the Cherries' third signing of the summer, after Ian Harte and Elliot Ward.