In Van Gaal, United have this summer appointed a new boss who has a considerable reputation for getting tough with his players, and he has already publicly declared his belief that the Red Devils' 19-year-old full-back Luke Shaw is not fit enough.
Pique clearly remembers criticism he received himself at an even younger age from Van Gaal when he was in the Barca youth ranks and the coach was in charge at the Catalan club.
Certainly it did not seem to do the 27-year-old any harm, and Pique - who has won two Champions League titles with Barca, plus the European Championships and World Cup with Spain, over the past six seasons - is confident Van Gaal will be "great" for United.
Speaking on Thursday at the St George's Park National Football Centre in Burton upon Trent, where Barcelona are having a pre-season training camp this week, Pique said: "I think he will be great.
"I didn't know him a lot because I was really young when he was Barcelona's coach, but he had a really good relationship with my grandfather, the former vice-president of the club.
"I had the chance to see him one day at my grandfather's house when I was 12 or 13 years old.
"He arrived at the house and he knew I was playing for the Barcelona youth team. He pushed me and I fell to the floor, and he said 'you are not tough enough to be a centre-back'.
"So, yes, he really is a disciplinarian, and I think he will do brilliantly here."
Manchester United manager Louis van Gaal (Reuters)
Without having made his senior Barca debut, Pique moved to United and played for them for four seasons, making just 23 appearances, before returning to the Nou Camp outfit in 2008.
There have been suggestions - including from Sir Alex Ferguson, the Red Devils boss at the time - that Pique was homesick, but he was keen to play that notion down on Thursday.
"No, the main reason was because Barcelona came to me and asked me to come back, and for me, Barcelona has always been my team - I always supported them," Pique said.
"So I asked Sir Alex if he would let me go back. When Barcelona are saying they want you back, you will be a first-team player, you will have a chance to play in the Nou Camp, with all the atmosphere - obviously I wanted to come back."
Pique also on Thursday had praise for United striker Wayne Rooney, his former team-mate.
"For me, Wayne Rooney is the best English player right now and definitely he would be in the top 10 (players in the world)," Pique said.
"He is a top-quality striker, the main player for Manchester United along with Robin van Persie, and he can play in every team in the world that he wants."
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