The Northern Ireland defender this week extended his loan deal from Manchester City until the summer, when he will be free to find a new club.
The 23-year-old is at his sixth loan club and is looking to put down some roots - and has not ruled out a permanent stay at Easter Road.
McGivern said: "I always wanted to stay and when the club said they wanted me I jumped at the chance
"My contract is up at the end of the season so it's a case of looking after myself and doing as well as I can between now and then. I will definitely be moving on from City in the summer. I'm at the stage of my career where I need to get out and settle down and improve myself.
"I have had quite a lot of loan spells and now is the time to settle down. You could say I'm in the shop window but I'm not looking at it like that. I'm just trying to do my best for Hibernian and hopefully we can have a really good season."
When asked if he could stay at Hibs beyond this season, McGivern said: "Possibly, yes. I'm just concentrating on doing as well as I can here and once the summer comes, whatever offers come my way then I will sit down and see what's best for myself."
Hibs begin the second half of their campaign at home to Dundee looking to move up from their fourth-placed spot in the Clydesdale Bank Premier League.
McGivern said: "We have got a really good squad here and we have a real chance to do something really positive this season.
"The fact Sparky (Leigh Griffiths) is staying as well is a major boost. I have really enjoyed my time here. The facilities are up there with the best in the league and the lads have been fantastic. I really feel a part of the squad, I don't feel like I'm a loan player. The fans have been terrific towards me and I want to repay them."
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