The England Under-20 captain made his debut for his new club in a friendly against Alfreton on Monday after penning a six-month loan deal.
And he admitted the Reds boss persuaded him to make the move to League One.
Coady told The Star: "Brendan really recommended that I came here, he was really pushing through the move.
"When he let me know United were interested he explained that I'd learn so much from playing under David Weir.
"I spoke to the Everton lads I know back home who worked with him (Weir) during his time at Goodison (Park) and they all said he's a brilliant coach.
"Brendan didn't have to persuade me to come but he did offer me the chance to go on pre-season with Liverpool to Australia and the Far East.
"But as soon as I knew what was happening, I wanted to join up with United straight away and get to know the lads."
Coady, who can play in defence and midfield, has made two appearances for Liverpool.