The hosts might also have key defender Kyle McFadazean absent after he came off in the 89th minute of Saturday’s 2-1 win over Bolton with a groin injury.
However, Callum O’Hare will be available for selection despite suffering a horror head injury in the second half of the victory over the Trotters.
Coventry’s win against rock-bottom Bolton – thanks to Maxime Biamou’s 90th-minute winner – keeps Mark Robins side one point and a place above Pompey in the table.
It will be a case of fourth against fifth when the two teams go head to head at Birmingham City’s St Andrew’s on Tuesday (7.45pm).
But Robins & Co might have to line up against the Blues without 10-goal striker Godden – who was the subject of Pompey interest in the summer.
Pompey bid a reported £425,000 for the then Peterborough forward but were not wiling to go any higher after Posh slapped a £750,000 price tag on his head.
Coventry did stump up the cash to bring the former Stevenage man in last August, with the striker scoring in the 3-3 draw with Pompey at Fratton Park the same month.
But Robins confirmed a groin injury could keep Godden out of the return fixture after he sat out the visit of Wanderers.
Speaking about the forward and MacFadzean to Coventry Live, the Sky Blues boss said: ‘Matty has this groin issue that he had previously that just flares up now and again and I am hoping he will be all right come Sunday and can train.
‘Kyle felt his groin so we tried to take him off but we wanted him to stay on because he’s so pivotal really.
‘Michael Rose was having a bit of a tough time (against Bolton) and I am glad he got that out of his system but we move on.
‘We move on with three points and are in for a good game on Tuesday and one to look forward to.
‘We have to recover well.’
Midfielder O’Hare, who is currently on loan from Aston Villa, clashed heads with Tota Nsiala in the 56th minute of Saturday’s win against Bolton.
He played on despite later requiring stitches to the wound suffered.
And with the 21-year-old not suffering any concussion, Robins confirmed he’ll be fit to face Pompey.
‘He (Callum) came off worse and you wonder how that happened with a 6ft 4in centre-half coming up against a 5ft 4 midfield player,’ added Robins.
‘But he’s tough and he gets up and has no fear.
‘He was chuntering to himself about doing it but they both had eyes for the ball.
‘The medical staff have been in to make sure he hasn’t been concussed and he hasn’t.
‘He’s right as rain but I shouldn’t joke about it because it’s a serious matter and if anyone loses consciousness you have to adhere to the protocol.
‘There’s no messing about but thankfully he’ll be available for Tuesday.’