The Pompey defender is closing in on a comeback from his ankle injury after returning to training yesterday.
Tomorrow’s trip to Accrington Stanley will arrive too soon for Burgess, however, who has been sidelined for more than four weeks.
But Cook feels the 24-year-old could be back in contention for next Tuesday’s FA Cup replay against Ipswich Town.
The Blues manager stressed Burgess will not be rushed back, though, after his period in the treatment room.
He will keep a close eye on the Peterborough man over the coming days before deciding the way forward.
Cook said: ‘Christian won’t be involved against Accrington.
‘You’ve got Adam Barton’s performance to think about and you then have Matt Clarke back in the squad.
‘We’ll maybe have a look at Christian for Tuesday night.
‘We’ll have a look at him after training well yesterday.
‘They don’t come back injured here. We make sure they are ready.
‘It’s been since Hartlepool, so he’s had four or five weeks out.
‘That’s quite normal for those kind of injuries.’
Danny Hollands has been served a blow with the news he is facing up to two months out with a broken leg.
Cook’s goalkeeping options remain an issue with both Paul Jones and Michael Poke out of contention.
Jones hasn’t played since September as he continues his rehabilitation from a knee injury.
Poke is still struggling with a hamstring problem.
But Pompey’s injury problems are, otherwise, largely relenting.
Michael Doyle remains in contention, despite continuing to manage a knee issue.
Cook said: ‘Michael Doyle’s right back in it.
‘Danny’s had his bad news and is out six to eight weeks.
‘Paul’s still with the physio, which is disappointing for him.
‘Michael Poke’s still got a hamstring.
‘Apart from that, everyone is out there training.’
– JORDAN CROSS