The defender has endured a stop-start opening to the season because of knee and thigh injuries and is not assured of a place in the team for the clash at Scottish Premiership leaders Inverness.
The Northern Ireland international missed the ill-fated Europa League games against Malmo and the opening Scottish Premiership defeat by Motherwell before coming off the bench during the loss to Hearts.
McGivern returned for the first three games of Hibernian's six-match unbeaten run before injury struck again, forcing him to miss wins over St Johnstone and St Mirren this month.
But the 23-year-old now feels fully fit and played the second half of Tuesday night's 5-3 League Cup win over Stranraer, which set up a quarter-final derby against Hearts at Easter Road.
However, both he and James McPake have been unable to force their way straight back in to the defence while Tim Clancy remains unfit, with Alan Maybury, Lewis Stevenson, Michael Nelson and Paul Hanlon in control of the jerseys.
"It's not been ideal start to the season," McGivern said. "I missed a chunk of pre-season and then the first couple of games of the season I wasn't really 100 per cent fit. I got back in the team and had another little setback.
"I missed two international games and one of them was against Portugal at home, which was a massive game.
"But I have had my stint on the sidelines now and am feeling good so hopefully I can get myself back in.
"The last couple of weeks I have worked with the physio and he has done a great job with me.
"I am just trying to get back in the side. The boys that have been in the side have been terrific and fully deserve to keep their place.
"It's up to me to work hard and force my way back in the squad.
"We've got a lot of strength in depth in the squad this season. Maybe we didn't have as much last season.
"But with the players the managers has brought in, I think we have two good players now in every position.
"Obviously that's what you need, you need to keep people on their toes and fighting for that starting place on a Saturday."