The Blues are in the spotlight as they continue to their push for a famous quadruple in Tuesday's Champions League round-of-16 first leg against Atletico Madrid on Tuesday, while City face Fiorentina at the same stage of the competition.
Both clubs have invested heavily in their squads this season and are also battling it out for the WSL title, but Hayes believes all the pressure and buzz is around her side.
"Everyone around Europe is loving the kind of pressure being put on Chelsea, the conversation being put out around this year, our team and what's expected of them, while Man City are not being spoken about," said Hayes.
"In terms of the placings in the League, as it currently stands, it's probably in part linked to the investment that's been made by both teams, but the continuity over a period of time, has put both teams in that position.
"Man City have probably invested more heavily than any other team this season, in new signings. So of course, the expectation should be on them as well as it is us because of the investment they too have made.
"Yes, they are going about it under the radar and doing it from a position where they're coming from behind, so the pressure is not necessarily placed on them in the same way it is my own team, but I embrace it.
"I don't want to be in another position, I don't want to be chasing, I want to be leading so we're happy to be where we are and happy that English clubs like Man City are also vying for titles because I think we are stronger together as an English group of teams than we are apart so our future's bright in this country."
The Champions League is the only trophy Hayes is yet to win with the Blues but they have been dealt the hardest possible last-16 draw, with Atleti the highest-ranked unseeded club, having knocked City out of the competition in the last two seasons.
But Hayes insisted she is doing nothing differently to prepare for the first leg at Kingsmeadow.
"The realities are, the more you ask me the same question, the more I'll say the same thing: it's just another game," she said. "To approach it any differently is to give it more weight than necessary. I've learnt by years of mistakes that to do it any different means you're probably thinking about the next game rather than one coming up.
"We have to make sure the only thing I'm thinking about is Atletico. To knock Man City out two years running, they've got threats, qualities. They're looking forward to the challenge of playing us. I have to prepare a team for that."
The match will be overseen by a team of Swedish officials, led by referee Tess Olofsson, and Hayes, who has previously been scathing of the standard of refereeing in the women's game, called by them to be "strong" and let the contest flow.
Asked what she was expecting from Atletico, Hayes said: "I think it's really important we get strong officials. Knowing in Europe the importance of making sure the officials are on top of the game is critical.
"I hope the game gets quality of officials it deserves to make sure the right things are being done in the game and that my players have the discipline necessary knowing that these games can be highly emotional.
"I hope we have the level of discipline and quality in our ranks to cope with that but that's the challenge for the squad. You have to be disciplined in these games.
"It can be different in different games. What may not be a foul in a WSL game can be in a European game. You need to have officials that have experienced top level European football to make sure it's a competition but not disturbed too much by break up by officials."