Rotherham are unlikely to make any more signings before the end of the month, according to manager Steve Evans.
Derby captain Richard Keogh has agreed a new three-year contract with the Sky Bet Championship outfit.
The 21-year-old has put pen to paper on a three-year deal, with the Terriers having the option of a further year.
Coady, who spent last season on loan at Sheffield United, made only two senior appearances for Liverpool, but appeared in their pre-season friendlies against Roma, Brondby and Preston and played in the Reds' recent Champions Cup semi-final win over AC Milan in the USA.
He made his senior Liverpool debut in November 2012 in a Europa League game in Russia against Anzhi Makhachkala and his Premier League debut at Fulham in May 2013.
Coady, who captained England Under-17s in their European Championship final win against Spain in 2010, made 50 appearances for Sheffield United last season, scoring six goals.