Gillespie, who was sold to Newcastle United as part of the deal that brought Andy Cole to Manchester in January 1995, made his Northern Ireland debut before his league baptism for the Reds.
Similarly, Brady had already played - and scored - at international level ahead of his United bow in the Capital One Cup win over Newcastle and has yet to figure in the Barclays Premier League.
"Robbie looks a really good, promising player," Gillespie told ManUtd.com. "I know he scored for the Republic of Ireland against Oman so he could follow the same path as me by making his international debut before his league debut.
"Good luck to him. I played against him in a friendly once when I was at Shamrock Rovers. He played well that night and looked a really good player so hopefully he can do well."