Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
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.