Derby are desperate to bolster their midfield options after an injury crisis at the iPro Stadium which has seen Will Hughes, Craig Bryson, Jeff Hendrick and Jamie Hanson all forced onto the sidelines.
As such, Derby have identified Butterfield as one of their top targets as they look to bring in the midfielder before the close of the transfer window.
The Rams have seen two previous bids turned down for Butterfield and they went back with a new offer of £3 million.
It was rejected by Huddersfield, however, who are determined to keep hold of the player and have placed a £5m price-tag on the 25-year-old.
Butterfield has established himself as a key member of Chris Powell's side since arriving from Middlesbrough last August and winning the club's Player of the Season.
Butterfield, who scored the equaliser in Tuesday's draw with Brighton Hove & Albion, still has three years to run on his current deal at Huddersfield and it remains to be seen if Derby come back with a fourth bid for the midfielder.