The 24-year-old, who came through the Rams youth system, started all four of Republic of Ireland's Euro 2016 games.
Hendrick has two years left on his current contract at the iPro Stadium after signing a four-year deal in 2014.
He has made 210 appearances for the Championship club, scoring 27 goals, since making his debut in April 2011.
Derby County have rejected a £3m bid for midfielder Jeff Hendrick from Premier League side Burnley, BBC Radio Derby understands.