Francis was an ever-present last season and will not be following top scorer Lewis Grabban out of the club, according to the club's chief executive Neil Blake.
He told the Cherries' official website: "We are not in a position anymore where we need to consider selling our best players," Blake said. "We especially wouldn't consider agreeing transfers to direct competitors towards the top of our division.
"Unfortunately our hands were tied with the sale of Lewis Grabban due to the release clause in his contract, but we will not be seeing any other players leave the club this summer unless Eddie Howe feels it is the right move for AFC Bournemouth.
"As Eddie has said publicly over the last few days, we are now in a position where we want to be adding the finishing touches to this season's squad and that is what I would like to be doing over the next few weeks."