Roberto Mancini's men suffered a surprise 1-0 defeat at the Stadium of Light on Boxing Day after Adam Johnson fired the Black Cats to victory.
Turner is expecting a difficult encounter against City after Norwich were edged out 1-0 by Chelsea at Carrow Road on Wednesday following Juan Mata's first-half winner.
But the centre-back says he and his team-mates will bid to emulate his former club Sunderland by getting something from the game.
He told the Canaries' official website: "It'll be a tough game against Manchester City - they're champions of the league and they've got world class players.
"It's only a few days after Chelsea so it's going to be tough, and they lost to Sunderland so they're going to want to bounce back and beat us. It'll be a tough game whatever happens.
"I think we need to play similarly to the games that we've won here [at Carrow Road], keeping it tight and hopefully create chances, score goals, and get something from the game.
"Sunderland have beaten them 1-0 a few times now and they obviously know what to do against them. We just hope to perform like we have done in recent weeks and hopefully get something from the game."
Turner is enjoying life at Carrow Road since his summer move from Sunderland and is happy with the defensive partnership he and Sebastien Bassong are developing.
He added: "I'm pleased with how I'm playing, and the partnership is going well.
"We're disappointed that we haven't kept a clean sheet in the last few games but I think things are going in the right direction with Seb and I, as well as defending as a team. We need to keep it going.
"I think we'd have taken 25 points after being halfway through. It was a difficult start for me personally but I like to think I've shown the consistent form I know I can produce."