Last season's UEFA Champions League semi-finalist crumbled to a 3-0 defeat at Real Madrid in midweek that stretched its winless run to four matches.
Di Francesco has diagnosed a lack of intensity and focus as the problem and will turn to Kluivert after omitting him from the matchday squad in Spain.
The winger, signed from Ajax to much fanfare, has only appeared three times as a substitute, but his coach insists the impending opportunity "shows the faith" Roma have in its new signing.
The Giallorossi boss Di Francesco expects the selection shake-up to help unlock the team's potential.
"We need a bit more fire in our bellies. It's my job as the coach to get that from my players," he said.
"The fans want to see it and it's right they should demand it. We need to play aggressively because that's the only way to get results.
"Everyone is trying to identify problems at the moment while I'm looking for solutions.
"It's not about fitness but conviction. We're not focused enough to step in and make up for a team-mate's mistake. I want them all to go that extra yard."
Kluivert could be joined in the starting XI by fellow teenager Nicolo Zaniolo, who was handed a shock debut against Madrid in midweek.
Di Francesco insisted there was no ulterior motive behind the 19-year-old's inclusion and that another appearance is possible at Bologna.
"Picking Nicolo Zaniolo in the starting line-up at the Bernabeu wasn't just about sending a message," he said.
"He could make his Serie A debut too. He's got plenty of ability. All my choices are geared towards what's best for Roma."