The pair sit together at the top of the Premier League table on 19 points after City defeated Brighton 2-0 before Liverpool secured a late equaliser to draw with Chelsea and preserve their unbeaten record.
"He's making the last steps, starting training in part in the next days".
It was Sterling's fourth goal of the season and incredibly the winger's 46th goal for City since he last netted for England in October 2015.
City were not expecting him to be available until late November, but his return could well come before this month's worldwide break.
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Eusebio Di Francesco's side have not won since their opening game against Torino in August, and travel Sunday to Bologna. UEFA says its disciplinary panel will judge the case of Ronaldo's first Champions League red card on September 27.
Guardiola admitted at the weekend that he faces a defining week in his season, after beating Brighton at home on Saturday thanks to goals from Raheem Sterling and Sergio Aguero. "I watched their game at Liverpool and they were very unlucky not to take a point", he said.
'These two games before the worldwide break will be so important for us.', Guardiola said.
And Guardiola insisted the attitude of his players has helped City reach the same - if not higher - heights than they did last term, a claim that will be tested in Sunday's visit to Liverpool. "He played good last game [the EFL Cup win at Oxford United], so [Saturday] he deserved to play again". It's a long time ago Man City was able to win at Anfield. It will be a really tough game, but we know that and we will try to do a good game'.
"You see it - the way we focus on every single ball", he said. Hopefully it's going to happen sooner or later'.
"Now it's Hoffenheim [on Tuesday in the Champions League], and after that we are going to prepare [for Liverpool], and after that we're going to prepare for Burnley".