The Argentine winger has been a mainstay in Alan Pardew's side this season and believes that the table-toppers face as tricky an away test as they could find in the Magpies
The Magpies have enjoyed a fantastic campaign in the league so far this season, and now find themselves within touching distance of fourth place with two games to go, just behind Tottenham on goal difference.
"If City want to get the title they will have to come to our place and win," Gutierrez told reporters.
"And that will not be easy for any team.
"They know how good we are and it is going to be massive."
The 28-year-old winger, who has been capped 22 times by his country, will come up against a few familiar faces from international duty during the fixture, with Carlos Tevez and Sergio Aguero set to lead the line for the opposition, something Gutierrez warns his team-mates need to pay close attention to.
"They have a few Argentinians in their squad who I know very well from our time together.
"Carlos didn’t have a great start to the season as everyone knows, but he has come back and been really, really strong in the last few weeks.
"I think he is fine now so it is very important that we don’t give Carlos or Sergio any space or they will punish us.
"We know we have to be fully focused for the full 90 minutes on Sunday.
"But we have been excellent at home this season and every team that comes here knows how difficult it is going to be for them."