The former Manchester United man has not featured for The Blues since November and underwent corrective surgery on his back in Argentina this week.
Reports emanating from South America have suggested the midfield maestro will be out for three months, but Ranieri believes that assessment is a worst-case scenario.
"Veron had an operation in Argentina this week," Ranieri said at the press conference to unveil new signing Scott Parker.
"In one week maybe he will come back to England.
"I have read in the newspapers that he will be out for three months, but I don't know about that.
"If everything is positive maybe he can make a return in one month."
Ranieri had news on other members of his squad currently in the Stamford Bridge treatment room.
"(Hernan) Crespo can start (training) next week with the first team," the Italian continued.
John Terry suffered a freak training incident at Chelsea's camp in Spain, but Ranieri revealed he has suffered no break.
However, the defender will have further assessments on his injury when the swelling subsides.
"I will speak to the medical staff about Terry and Robert Huth," added Ranieri.
"The scans say nothing is broken, which is important, but we will have to see if he can run or not."
