Unzue is one of the two leading candidates to succeed Luis Enrique, who announced this month he will leave at the end of this season, along with Athletic Bilbao coach Ernesto Valverde.
Unzue, a former Barcelona goalkeeper, worked as the Catalan club's keeping coach from 2003-10 and again in the 2011-12 season after an unsuccessful stint in charge of Numancia. He became Luis Enrique's number two at Celta Vigo in 2013, joining him at Barca in 2014.
Barca have won eight out of 10 trophies under Luis Enrique and could yet win a second treble in three years, with the club second in La Liga, in the King's Cup final and in the last eight of the Champions League.
"Unzue knows everything about the club very well and how it works, he worked at the club for a long time and is working with us now. He's a qualified and experienced coach and is now excited about finishing the season and helping us meet our objectives," Iniesta said.
The Barca and Spain midfielder also praised Valverde, who was reportedly close to becoming Barca coach in 2013 when Tito Vilanova was forced to leave due to ill health but had already committed to taking charge of Athletic.
"At the moment these are hypothetical conversations but if that was the case, he'd be a great coach. He has always done well wherever he has been. He has a recognisable style," Iniesta added on Valverde, a former Barca striker.
Barca defender Pique is also backing Unzue.
"He's spent many years at the club, not just with Luis Enrique but also with Pep and I'm sure he would be a good candidate," Pique told reporters.
Croatian midfielder Rakitic said Unzue had a good understanding with the players.
"I have a very good relationship with him, he knows us very well, we have maximum confidence in him," Rakitic said in an interview with radio station Cadena Ser on Friday.
"Luis Enrique has his staff but Unzue has his own ideas. It's the same philosophy, but each coach has his own style."
(Reporting by Richard Martin, editing by Ed Osmond)
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