The 19-year-old looked set to play a part in City's first-team this term after participating in the club's pre-season tour to the United States.
However, he's since be sidelined as City hunt down their first domestic title for 44 years, and Bouskouchi says a move to United could be the kick-start his career needs.
"These days, Manchester City are chasing titles and major trophies," said Veseli's agent Bouskouchi.
"It is difficult for them to have faith in youth because they obviously feel experience is the best way for them to get where they want to go.
"But that attitude didn't help Freddie, who just felt like he wasn't progressing. On that pre-season tour, both Roberto Mancini and - director of football - Brian Marwood said how well he had done. But since then, nothing."
"Freddie spoke with several clubs, here and abroad," Bouskouchi added.
"But he wants to be a top player in England and when Sir Alex spoke to him, it made such an impression.
"He is a difficult man to say no to and his track record was enough for Freddie to feel he was making the right choice to join United."
The Swiss youth international will play with Warren Joyce's reserve side prior to being promoted to the first-team.
Veseli can be optimistic he'll earn a promotion to the elite at United, with the likes of Danny Welbeck and Tom Cleverley having recently earned call-ups, while the success of Phil Jones, also 19, will work as added incentive for the former-blue.
Veseli also has an eye on this summer's football tournament at the Olympics.
Bouskouchi added: "First his challenge is to establish himself at reserve level, then push on for the first team.
"But the Swiss Federation have also been in touch and they are keeping track of him. However, they have said Freddie must at least be involved at reserve team level before they could consider him for the Olympics."