The Reds have made a positive start to their campaign, and currently sit second in the division below Arsenal on goals scored.
However, Jones feels that the club should not deviate from their original target of making it back into the Champions League places, and believes a title challenge is premature.
"At the moment, we don't want to get too carried away. It's been a long time since we've won the league," Jones told The Sport Review.
"I think top four should be the aim – and maybe see if we're up there [at the top] around Christmas time. Now, if you can get into the Champions League, it's a good result. Top four is good but let's see where we stand after Christmas.
"Nowadays, you look for a top-four finish. In my day, if you finished fourth, it was a disaster."