The striker fell down the pecking order at Old Trafford last season under Ole Gunnar Solskjaer and was sold by the Red Devils to Inter Milan in the summer.
However, Federico Pastorello said his client was "happy" playing under Solskjaer and that the opportunity to move to Serie A was the deciding factor, per Sky Sports.
"The relationship with Ole was good at the end. There were maybe some issues tactically because he is a number nine striker and sometimes the coach preferred another amazing player in [Marcus] Rashford.
"The move was not really linked to some particular issue at Manchester United, but really to try a new experience.
"He was happy at Manchester United. He liked the fans a lot and United are in the top three or four clubs in the world.
"To play for them was amazing and he was happy about that, but I think he wanted to prove himself in another championship and he needed another challenge."
The dismissal of Jose Mourinho as United boss in December 2018 had a profound effect on Lukaku's standing at Old Trafford, and Solskjaer's arrival changed the stylistic principles of the starting XI.
The Norwegian favoured a fluid attack, with three raiding forwards who could interchange during counter-attacks, and Lukaku's game could not be utilised.
United chose to give Anthony Martial the No. 9 shirt he lost in 2016 to Zlatan Ibrahimovic, and Lukaku was shown the Old Trafford exit after failing to impress from the bench.
In his final season at United, Lukaku scored 12 goals in 32 Premier League appearances but was forced to rise off the bench 10 times.
Lukaku has thrived at Inter under the guidance of Antonio Conte, and the Belgian has impressed in a 3-5-2 system partnering Lautaro Martinez.
Lukaku has netted 10 Serie A goals in 15 games and promises to further expand his numbers as the first-choice striker.
Conte captured the Italian title with the Old Lady in 2011-12, going on to win Serie A three consecutive times, and then won the Premier League in his first attempt during 2016-17.