The Cherries rejected two attempts by the Rams to lure the 29-year-old to the iPro Stadium this summer.
Francis has made over 100 appearances for Bournemouth since joining them, initially on loan, in late 2011 but he insists his place is with the club who started this season with an impressive 4-0 win at Huddersfield.
“Derby is a club close to my family and I have a lot of friends up that way," he told the Bournemouth Echo. "It was something I was aware of over the summer but the valuation was never met and it didn’t get far at all.
“It was flattering that a club of their calibre showed an interest but I think that’s down to what we’re doing as a club, as a group of players and how the manager has got us playing."
Francis' nomadic career before Bournemouth included spells with Bradford, Southend and Charlton, but now he has eyes on a first stint in the top flight with the side managed by Eddie Howe.
“I would probably say I had the chance to show what I was about before but I let it slip when I was younger. I played at a couple of Championship clubs and through fault of my own I didn’t grab my chance with both hands or relish the challenge like I am now.
“I am the happiest I have ever been in my career. I’m at a good age now and I want to be playing my best football at the highest possible level.
“I wouldn’t be saying that and I wouldn’t be at this club if I didn’t think we were good enough to kick on and get to the Premier League.”