Reports emanated over the weekend that right-back Francis, 29, had been the subject of interest from last season’s beaten play-off finalists on the back of his consistent displays for the Dean Court club.
The former Charlton Athletic defender had played every minute of every match during Cherries’ return to the second tier before sitting out the first half of the campaign closer at Millwall.
Francis, who provided more assists than any other Cherries player last season, had his fine form recognised by supporters when he won the Daily Echo's Micky Cave Trophy, the player of the year award voted for by fans.
And having today confirmed the Rams’ interest in Francis, Blake took the opportunity to reiterate boss Eddie Howe’s mantra that Cherries had no intention of selling their prized assets.
"We are not in a position anymore where we need to consider selling our best players," Blake told the club website.
"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 past 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."
Derby County have declined to comment on Blake's announcement according to the Derby Telegraph.