The Spaniard trained yesterday, and the club are giving Rodri every chance to prove his fitness ahead of the trip to Anfield, according to the Daily Mail.
The 23-year-old hobbled off the pitch against Atalanta in the Champions League on October 22.
It was later revealed that he had picked up a hamstring problem, and faced being on the sidelines for up to six weeks.
But, with Rodri back in training earlier than expected, him being passed fit to start would hand Guardiola a major boost against Liverpool.
If the defensive midfielder doesn’t play, Man City will have six first-team players unavailable.
Leroy Sane is expected to return from a ruptured anterior cruciate ligament injury in February, while Aymeric Laporte still faces two months out of action.
Oleksandr Zinchenko had surgery on his knee at the end of last month, and may have played his last match of the calendar year.
Elsewhere, David Silva has a muscular injury which sees him miss the Anfield trip.
And goalkeeper Ederson picked up a knock in midweek against Atalanta in the Champions League.
Rodri was signed from Atletico Madrid this summer, in a £63million deal.
He appeared in all of City’s first nine Premier League matches of the season, before picking up his injury.
City head to Anfield knowing that a defeat will take Liverpool nine points clear at the top of the table.
Guardiola’s team could drop down to fourth in the Premier League table if other results go against them.
But, a win would see the gap reduce to just three points, with Liverpool still facing a trip to the Etihad Stadium for the reverse fixture next April.
The Citizens haven’t won at Anfield in 16 years, and Liverpool haven’t lost at home in the league since April 2017.