The defender was substituted in the 68th minute of Tuesday night’s 3-2 win at Barnsley because of a groin injury.
He sat out training on Thursday as the Blues began their preparations for the visit of the Imps to Fratton Park.
A fitness test has been scheduled for Friday to determine the 27-year-old’s availability – but Jack Sparkes has been put on standby to start at left-back if the result is negative.
If that is the case, Lincoln’s visit will be just the second time this year that Ogilvie will have been unavailable for selection in the league.
His absence will represent a big blow, with the former Gillingham defender playing a key role in a defensive unit that has conceded just five League One goals this season – a record bettered only by Exeter (4).
That fact isn’t lost on John Mousinho, who believes Ogilvie will be determined to make himself available as soon as possible.
The Pompey head coach told The News: ‘Connor is struggling with his groin. He’s going to be touch and go for the weekend.
‘We left it off today just to see how it would settle down but it’s still a bit sore and we’ll give him a fitness test tomorrow and see how he shapes up.
‘He’s played such a pivotal part of everything we’ve achieved since I came into the football club.
‘He’s missed just one game towards the back end of last year and didn’t play against Morecambe at home, so apart from that he’s been absolutely flawless in terms of his ability to come in and play games.
‘So, yeah, Connor is very robust and I’m sure he’ll be back as soon as he can.’
While doubts exist about Ogilvie’s fitness, fellow defender Sean Raggett is expected to return to the squad for the visit of Mark Kennedy’s side.
The 30-year-old wasn’t involved in the midweek win at Oakwell because of a foot injury. However, the centre-back is back to full fitness and ready to compete for a place in Mousinho’s starting XI.
‘Raggs should be absolutely fine. Raggs trained today so he’s absolutely fine,’ added Mousinho.
‘That was one that just needed to settle down. He took a knock to the bottom of his foot.
‘He was willing to dose himself up and get out there (against Barnsley) but we knew we wouldn’t be able to rely on him for anything more than 10-15 minutes.
‘At that stage, a player is not really fit if you want him to be involved so I thought it was the right decision, considering he trained today and he’s available for the weekend.’