The Royal Blues have never won the Bundesliga since its inception over 50 years ago, and the United States international says it must be their ambition to end that barren run.
"This team has got the potential to compete at the very top," he said. "We shouldn't just be talking about second to fourth place.
"Our aim has got to be to challenge for the title."
Schalke have gone close to winning the league several times in recent years, most memorably in 2001 when they were denied by a last-minute goal from Patrik Andersson on the final day of the season which saw Bayern Munich snatch the title.
After winning the treble last season, Bayern are once again going to be the team to beat, but Jones is ready for the challenge.
"What more could you want than to be hunting this team down?" he said in Kicker magazine.
"It's great when everybody sees you in this role before the season starts."
Schalke clinched a place in the Champions League only on the final day of last season despite being Bayern's nearest challenger up until Christmas.