Amakhosi are level on points with League leaders SuperSport United, albeit in fifth place on the table due to goal difference, and although they remain in Telkom Knockout contention they exited the MTN8 at the semi-final stage last month courtesy of fierce rivals Orlando Pirates.
"Everyone wants to beat the champions," Gaxa told his club's official website.
"It has been a roller-coaster for us at the start of this season but we have started picking up.
"We are not far from the log leaders. We are fifth in the log and only goal difference separates us from the leaders.
"Coming to this season, we knew it was not going to be easy. It has not been smooth but we will continue to work hard."
Chiefs next face Free State Stars in the last-eight of the Telkom Knockout on Sunday, with Gaxa relishing the upcoming challenge at Charles Mopeli Stadium.
Gaxa said: "At Chiefs it is not about the opponents. We respect Stars but we are focused on Chiefs.
"We know that this is a massive game not for us only but for them as well.
"We are looking forward to the challenge and to play good football. They are a good side and they also play good football.
"On Sunday we will do what we normally do best and fight for the club,"concluded the Bafana Bafana right-back.