"It's still too early to say who will be the favourites, but I have been impressed by Liverpool so far," Koeman was quoted as saying by ESPNFC at the launch of the Kick It With Help anti-smoking campaign.
"Maybe that is not what you might expect the Everton manager to say, but they have been playing some very good football and deserve to be at the top. They have goals in their team and this is what all successful sides need.
"Of course, they can be champions this season, they have a good chance, but they are not the only contenders."
"My Everton team has played Manchester City and Chelsea in the last few weeks and both were very impressive. We managed to draw at City, but you could see the quality of these teams."
"Then we all know what happened at Chelsea, as we lost 0-5 and they put in a very good performance. It was difficult for us, but you have to be impressed from their side, so maybe they can also have a chance."
Koeman also said Manchester United should not be ruled out of the race despite a stuttering start to the season under new manager Jose Mourinho.
"I see this as a very open title race," he added. "You have four or five teams in contention and even though Manchester United have had some problems so far, they can still go on a good run and put some wins together."
"United have a new manager and they will improve in what is an unpredictable EPL season. People expect someone like this with such a big record to win games instantly, but it is not so easy. Of course,they can come back because they have some top players and a very good manager."
Koeman said his team's aim this season will be to push for a place in a European competition for next season.
"It is a long time since Everton were winning trophies and challenging for the title in England, but that is what we want to do," Koeman said.
"This is a very big club and the aim is to be in the top positions again, challenging for the important places in the Premier League."
"It takes time when you come to a club to get everything you want in place, but I understand that in this game now, you do not always have the time.
"Results are very important and while we say there should be more patience, that is just not how this game works now."
"Long-term projects are no longer possible if you do not have success quickly and even though most supporters appreciate a manager should have some time, others can put pressure on the owners and decision makers at clubs who hire and sack managers."
"When you have a result like we had against Chelsea, there will be criticism if you are at a big club like Everton, but you need to accept that and try to come back."
"The ambition this season will be challenging for European football. We have introduced some new players last summer and it takes time to find the right balance in the team and to find consistency, but I feel it is not far away."
"If we are competing for a place in the Europa League in my first season here, then that would be a good achievement.
"I think this is possible, but we can see a lot of teams with the same ambition as us in the Premier League, so it will not be easy," he added.