Their chances seemed to have disappeared in the last two games, losing at home to Chelsea and then throwing away a three-goal lead in the last 11 minutes at Crystal Palace.
Now they must beat Newcastle at Anfield and hope 12th-placed West Ham can somehow win away to City, who have beaten them three times this season, by an aggregate of 12-1.
In the aftermath of the Crystal Palace collapse, Rodgers predicted that City would win their remaining two games to deny Liverpool a first title since 1990.
They duly defeated Aston Villa 4-0 on Wednesday but two days later Rodgers had changed his tune a little, telling a news conference: "It's certainly not over. West Ham have got some really talented players and if you can go to Tottenham and win 3-0, you can certainly go to Manchester City (and win)."
Liverpool will be hoping for a favour from Andy Carroll, the striker they sold last summer to West Ham after spending the previous season on loan there, although he has scored only two goals since returning from injury in January.
"They've got a really good defensive record with 14 clean sheets, so it shows they're a really difficult team to play against," Rodgers said.
Whatever happens on Sunday, however, the manager said that Liverpool, who finished only seventh a year ago after his first season in charge, can be proud of their efforts and will be even stronger for the next campaign.
"I want to congratulate my players on this season, we've had a remarkable season and the players have put Liverpool on the world map again," he said.
"If we end up finishing second to the richest team in the history of sport it really shows the progress we've made here. It's a huge compliment to be even considered for the title.
"I think we'll improve dramatically next season with the young players that have come through. So for us it's only the beginning."