However, Forest appear to have seized the initiative in tabling an offer for the 30-year-old, who has fallen out of favour at the Vitality Stadium in recent times.
Grabban first joined Bournemouth in 2012, scoring 35 goals in two years before being signed by Norwich City in 2014.
After struggling to adapt to the Premier League following the Canaries' promotion, Grabban returned to Bournemouth in 2016. However, the striker has continued to struggle in the top flight and has made just 15 appearances in his second spell at the club, spending much of his time on loan at Reading, Sunderland and Aston Villa.
Grabban scored 20 goals in 35 appearances for Sunderland and Aston Villa in the Championship last season and finished second in the race for the Golden Boot, suggesting that perhaps he is better suited to life in the second tier of English football.
Bournemouth already have the likes of Joshua King and Jermain Defoe as options up front, meaning a return to the first team in the near future appears unlikely for Grabban.
Grabban began his career at Crystal Palace and has gone on to have something of a journeyman's career, representing 11 different clubs to date. He was called up to the Jamaican national side in 2015, but is still yet to make an international appearance.