Both Forest manager Dougie Freedman and chairman Fawaz Al-Hasawi have stated their desire to hold on to the former Sheffield Wednesday man, so influential alongside Britt Assombalonga in his first season at the City Ground.
Bournemouth may not have Forest's history behind them but they do have a place in the top-flight of English football with all of the lure and lucre that currently comes with it. That means that, if they do put in a £7.5m bid it will be extremely difficult for the Reds to reject it.
Antonio was part of the side that drew against Mjallby AIF in Nottingham Forest's second pre-season game of their trip to Sweden on Sunday.
Trialist forwards Nicky Maynard, Paul Taylor and the returning Darius Henderson all featured at various stages of the match in which Chris Burke scored the goal for Forest.