The Rams are understood to have failed with two bids to sign the 29-year-old last month.
Despite revealing that a switch to Derby might have been hard to turn down, Francis is optimistic about the season ahead with Bournemouth.
"Derby is a club close to my family and I have a lot of friends up that way. It was something I was aware of over the summer but the valuation was never met and it didn't get far at all," he told the Bournemouth Echo.
"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 joined Bournemouth in 2012 following a two-year spell with Charlton Athletic.