Petrucci has started both Posh's Championship fixtures since joining the club on a month-long deal on January 9.
Ferguson signed defender Scott Wootton from United on the same day on a deal until the end of the season and hopes to keep Petrucci at London Road for the same length of time.
"He is, by definition of where he came from, a very good footballer and he loves being at this club," said Ferguson after his side's 1-1 home draw against Hull on Saturday.
"We only have him for a month at first, but I will definitely try and extend the loan."
Ferguson added: "We have brought Davide Petrucci here to play. He got very frustrated with himself in the second-half (against Hull) which is why I took him off, but we have to bear in mind that he has never been out on loan before."