The 19-year-old is reportedly on the radar of the Premier League pair and could be at the centre of one of the summer's biggest bidding wars.
McBride believes that Anfield will provide Pulisic with the best surroundings to develop his game, though Real Madrid will trump all other interested parties should they show a concrete interest in the talented forward.
"Choosing for him a club that would help him develop his style and his skillset is going to be a necessity," he told ESPN. "When you talk about some of these bigger clubs, they don't necessarily play the same type of soccer they play in Dortmund.
"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.
"The exciting part of going to Real Madrid, where every single player on the field around you is world class, it's a desire you sometimes can't turn down."
McBride spent time in the Premier League with Fulham and Everton, while also representing the USA close to 100 times.