The Citizens were linked with the 24-year-old at the start of the month, only to shelve plans of making an offer until the end of the season.
Guardiola's stance has changed, however, which the Manchester Evening News suggests is partly down to the injury sustained by the versatile Fabian Delph last week.
Delph has been used mainly as left-back cover this season, featuring 23 times in that position, but he can also fill in for Fernandinho in the middle of the park.
On top of the Englishman's layoff, which is expected to keep him out for at least another few weeks, the report claims that Yaya Toure is no longer seen as a sufficient option after being left out of the matchday squad against Newcastle United last time out.
Fred, who himself has experience of playing at left-back, is now said to be City's only serious target for the remaining nine days of the transfer window and talks with Shakhtar are planned.