McGovern, 31, joined Celtic as a 17-year-old back in 2001, having emerged as a young prospect with Enniskillen Town United in his native Northern Ireland, but he failed to make the grade with the Bhoys.
A move to Dundee United also failed to reap any rewards for McGovern, but he established himself as a first-team player with Ross County, Falkirk and now with Hamilton Academical, having signed for the club back in the summer of 2014.
The seven-cap Northern Ireland international is out of contract this summer though, and The Scottish Sun report that both Aberdeen and Rangers are keen to land him on a free transfer this summer.
McGovern will be battling with Roy Carroll and Alan Mannus for the No. 1 jersey for Northern Ireland at Euro 2016 this summer, and whilst he may look to wait and impress in France before committing to a deal, it's believed that he is open to offers right now.
It's suggested that Rangers are willing to offer an impressive deal to McGovern in a bid to ward off rival interest, with Mark Warburton keen to bring him in as competition for first choice stopper Wes Foderingham.
Cammy Bell is unlikely to stay at Ibrox whilst January signing Maciej Gostomski is out of contract, and a new deal for the Pole looks unlikely right now, making McGovern a possible target - but they will certainly face competition to sign him on a free transfer this summer.
Would you like to see Rangers sign McGovern this summer?