Jakobsen had started every game this season but has missed City's past two fixtures due to a quad complaint.
The Danish defender failed to complete a full training session on Tuesday, leaving the track early.
The odds are relatively even for Friday's game in Newcastle. City have won there twice this season but with Jakobsen in their side on both occasions.
Jakobsen's defensive teammate Osama Malik, who also missed several weeks this season with a similar injury, provided an update on the captain after training.
"I think there's still some hope that he'll be part of the squad," Malik said.
"He's a very important player for us. Even if he's not playing, he's important to have around.
"He's a leader in our team, so I'm sure he'll play some role."
Jakobsen's absence has coincided with Malik's return from a quad injury, having missed two months of action.
Malik missed seven games, having sustained the injury in the warm-up prior to the 4-0 home loss to Sydney but has settled back in with ease.
"It was a bit of a long road," Malik said. "I was out for a few weeks.
"It's been nice to come back into the squad at such an important time of the season.
"To be honest, I'm feeling really good."