The 19-year-old joined the Bundesliiga outfit's youth team in 2015, when the current Reds manager Jurgen Klopp was in charge at the Signal Iduna Park. He made his first team debut in January 2016 and has been a regular figure in their starting lineup.
Pulisic has started in 17 league games, while he came off the bench on two occasions for Dortmund this season. He has scored three goals and registered two assists in the process. The attacker's form has seen him being linked with United and Liverpool, reports the Manchester Evening News.
McBride believes Liverpool's playing time style will suit Pulisic better than United and also help him develop as a player.
"It all depends. Choosing for him a club that would help him develop his style and his skillset is going to be a necessity. When you talk about some of these bigger clubs, they don't necessarily play the same type of soccer they play in Dortmund," McBride explained, as quoted by the Liverpool Echo.
"The thing that's always in the back of your mind is the desire to play at one of the biggest clubs - they are monster clubs, all of them are - and the fun of moving to a different club and working through the process of making it there.
"I would make sure the club plays the style of soccer I play. If you're going to Manchester United, you know you're not going to be on the ball nearly as much as you are at Liverpool or Real Madrid."
Pulisic has already revealed he was a boyhood United fan and refused to rule out a move to the Premier League in the future as United and Liverpool continues to be linked with a player. McBride has backed the United States international to leave Dortmund, if there is a concrete interested in his services later in the summer transfer window.
"These are big decisions for you as a player, especially at such a young age. One, he needs to play, which makes him a candidate to stay," the ex-Everton and Fulham striker said.
"He's also in a pretty large sized club with an understanding of the structure, an understanding of the players, an understanding of the style. All those will give you an argument to not leave.
"But as a player, you always want to push the envelope. You always want to make sure you are challenging yourself to the best of your ability to grow as a player. If he feels there are options there, I could see him move. He's too mentally strong and mature (to get lost), in my opinion."