Caligiuri and Muller were teammates at Mainz and Greuther Furth, but the former has now moved on to a new challenge at Braunschweig.
"Yes, [Nicolai joined Mainz at the right time]," he told Bundesliga.com. "He was so consistent with Furth in 2. Bundesliga and proved over several seasons what a good player he is.
"It was time for him to take the next step. Mainz was predestined for him. The club had always recognised his potential and he's repaying them right now.
"His pace [and] his quick dribbling [are his key skills]. He has also become a much better finisher and has learned to stay calm on the pitch - he now knows when to speed things up and when to keep hold of the ball."
Caligiuri made 74 league appearances for Mainz during his time at the club.