Speculation has risen about Martino's future at the club after a patchy run of form that has seen the Catalan giants slip to third in La Liga.
Barcelona are four points behind leaders Real Madrid, but face their rivals in Sunday's much-anticipated Clasico.
And while defeat could spell the end of their title chances, victory would be a huge boost to Barca's season.
Iniesta told a press conference on Thursday: "Every day he (Martino) is motivating us. He is a new manager and different. Every manager is different.
"His presence and instructions…his way of understanding football, it motivates us.
"You need the manager to guide the team but the motivation to play and to win and to continue winning, that comes out of the group rather than the manager.
"We've had so many experiences within this team and we've managed to win year after year so I think we are doing the right thing.
"I'd love him to stay with us. He is very capable of being here."
Martino has guided Barcelona into the last eight of the UEFA Champions League and the club will find out who their quarter-final opponents are on Friday.
Iniesta is excited ahead of the draw and would prefer to play an attacking-minded team.
"We say this every year – we look forward to draws, we like to see which team we will play, it's always fun," he added.
"I think we're really excited about it.
"It's great that we're amongst the last eight teams. All the teams in the competition are very strong.
"There's different styles, some prefer to hold the ball, others prefer to play defensively and play on the counter attack. You never know which opponent you want.
"I personally prefer teams that like to take the initiative but I also know that this is the team that often beats us. Different styles are the attraction of football though."
