Grabban, who was the club's top scorer last season, was sold to Norwich City last month.
Wilson, who joined Bournemouth from Coventry City on Friday, has said that he will focus on his own performances.
"I have not come here to replace anybody. I've just come here to score goals for the team," he told BBC Radio Solent.
Wilson scored 22 goals in 41 games for Coventry in League One last season.