Liverpool's 18 championships put them two ahead of United, who visit Anfield on Sunday.
"We have won the FA Cup more times than anyone (11) so you get a certain pride in that and it's the same for Liverpool," the 65-year-old Ferguson told reporters. "They have won the title more times than anyone and they'll be proud of that.
"The chase will always be on to be number one in your country. For us there is an expectation and for Liverpool there is an expectation and I hope before I leave we can get to that position."
Premier League champions United have won the title nine times in the last 15 seasons.
Liverpool have not won the league since 1990 and even though they became European champions for a fifth time in 2005, Ferguson believes domestic honours best represent a team's success.
"Winning the league is without question the barometer of our game," he said.
United are second in the table, one point behind leaders Arsenal who host third-placed Chelsea on Sunday. Liverpool are in fourth spot, seven points off the pace.
Ferguson also said he expected former England midfielder Paul Scholes to resume full training in six weeks after having knee surgery in October.
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