Nardiello has scored four goals in seven appearances during a second loan spell at Bury after joining from Rotherham United last month.
The 31-year-old scored a stoppage-time equaliser in Boxing Day's 2-2 draw with Scunthorpe United and Flitcroft is keen to see Nardiello stay with Bury.
"With so many loan signings at the club, we'd like to make the deal with Danny permanent to take the weight off the loan situation," said Flitcroft after the Scunthorpe game.
"Daniel Nardiello is a David Flitcroft-type player and certainly the kind of player I am trying to bring to the club.
"If you can play through Daniel Nardiello and get him slid into the box with passes like that then there are a lot of goals in him.
"That's the plan. I want to work with Danny - he knows that."