Pitta, who is on the Injured Reserve-Designated for Return list, has practiced since Nov. 20.
"We'll go through this week and see how he does," Harbaugh said Monday. "If he can play, he will. We want to get him up. That's our goal. It's not 100 percent certain at this point."
The Ravens' three-week window to decide whether to activate him to the 53-man roster or keep him on IR ends Dec. 11. If they want him to play against the Vikings, the team would have to activate him before 4 p.m. ET Saturday.
Pitta dislocated his hip on July 27, and the Ravens have missed him in the offense. In 12 games this season, Dallas Clark and Ed Dickson have combined for 47 catches for 554 yards and three touchdowns. Last season, Pitta was second on the team with 61 receptions for 669 yards and seven touchdowns.
Pitta ran around well last week, according to Harbaugh.
"[The decision will] probably come down to the end of the week," Harbaugh said. "I've got a pretty good idea that he's doing well. It's just a matter of how well. Is he feeling good enough? Do the doctors feel like he's ready to play? That's what it's going to come down to."
Harbaugh was more definitive about the injury status of cornerback Jimmy Smith, who suffered a concussion on his goal-line hit of Steelers running back Le'Veon Bell. Because Smith didn't return to Thursday night's game, backup Chykie Brown was pressed into action and was the defender on the Steelers' failed two-point conversion, which would've tied the game with 63 seconds remaining.
"Everything looks really, really good for Jimmy. He should be fine," Harbaugh said. "You never know with that, but it looks like he'll be able to practice Wednesday. So we feel good about that."