The Reds continue to go from strength to strength under Jurgen Klopp and have spent upwards of £175m this summer on four high-profile signings.
"When we look across Stanley Park, no matter what any of us say, and see the big German (Klopp), the style they're playing, and the way they have invested again – it's nervous times for Evertonians," Barton told talkSPORT.
"I honestly think they could get really close to their first title in 20-odd years. It will be really close."
Liverpool last won the English top-flight championship in 1990.