The Reds are currently top of the table during the international break.
Kelleher said: “Obviously the standard is crazy at the moment. You have (Manchester) City and Arsenal who have shown in the last few seasons they are title contenders, and we’re trying to match them.
“But you look at the schedule and every game is a difficult game and that just shows the standard of the league. You can’t relax or take your foot off the pedal in any games because you won’t get the result you want.
“I think the quality right throughout the league is really good, and I think personally it's the best league in the world.
“We need to be ambitious, we definitely have the quality within the squad to challenge for a title. It’s easy saying that – you need to obviously back it up.
“If we want to compete we need to be on a similar level to them and keep these performances up and, most importantly, keep the results up.”