Manuel Pellegrini's side have racked up 41 goals in 10 home games in all competitions during a fearsome run of form on their own patch.
The likes of Sergio Aguero, Alvaro Negredo and Jesus Navas ran amok in the 6-0 demolition of Tottenham last weekend and while Laudrup acknowledges the size of the task facing Swansea, he knows they must not shy away from the challenge.
"City are the best home team in the league with 26 goals in six games so we know it will be a tough afternoon, but we can only surprise people there," the Swansea manager said.
"Everybody expects City to win by a few goals because they've done that against everybody including Manchester United and Tottenham.
"So I think we will go there to do the best we can to get something out of it, and whatever happens we will still present a competitive team.
"You can't play with fear in football. There is a lot of respect, you have respect for everybody, the ones on top and at the bottom, but never fear."
Laudrup has also urged striker Alvaro Vazquez to make the most of his chance to shine with Wilfried Bony and Michu sidelined by injury.
Record signing Bony limped out of Thursday's 1-0 Europa League defeat to Valencia with a hamstring injury which will keep him out for several weeks; the Ivorian will undergo a scan in the coming days to determine the exact extent of the problem.
Michu is also unlikely to return from his ankle injury in time for Sunday's game, although he has taken part in some light training as he targets Wednesday's meeting with Newcastle.
That means Vazquez, who is on a season-long loan from Getafe and has yet to score for the Swans in 10 appearances, will lead the line.
The 22-year-old was denied a goal by an incorrect offside decision against Valencia, as well as having another effort cleared off the line.
Laudrup said: "It is true we have injuries to our strikers but we will cope with that.
"Alvaro came close against Valencia and now this is his chance, his possibility.
"Of course every player wants to play, not because a team-mate is injured but that is part of football. When one goes out another has the chance to go in, that's how it works."
Laudrup also confirmed Wayne Routledge will return from a calf problem against City, while Pablo Hernandez made just his second appearance since September 1 on Thursday.
"Well, we still have at least 11 players," joked Laudrup when asked about his selection options for Sunday.
"But, to be serious, we lost two players against Valencia but have another two back.
"Pablo played for the first time in some weeks and Wayne will be back as well so we will have an 18-man squad as we did against Fulham, just with other names."
Source: PA
Source: PA