Gundogan played alongside Mkhitaryan at Borussia Dortmund and the duo have both made moves to the Premier League this summer.
Mkhitaryan is expected to put pen to paper on his move to United in the upcoming days after passing his medical with the club late last week.
“Henrikh has been at Dortmund for three years. The first two years were not so easy for him, to be honest,” Gundogan was quoted as saying by Manchester Evening News..
“He’s a player who needs self-confidence, who needs to play every time and prove himself to get better and better. At this time, we were not so successful, so it was not easy for him to adapt. He had a few problems.
“But when you see how he played last year, it was really incredible. Maybe he was the most important player for us last year.
“If he can go on like this, he will have a big, big impact for Manchester United, and a big plus. I wish him the best, and to stay healthy.”
Gundogan missed out on Euro 2016 this summer after suffering a knee injury during training. The same injury came close to costing him a move to the Premier League giants. The midfield playmaker also missed the 2014 World Cup in Brazil due to a back injury.
Gundogan initially joined Dortmund from Nuremberg in 2011 under the stewardship of Klopp and helped the Bundesliga giants reach the 2013 Champions League final.
The midfield playmaker provided seven assists and three goals in 40 appearances for Dortmund last season.