The 31-year-old was linked with a move to Leeds United last month, as Norwich and Wigan join the race.
The 31-year-old's stock has risen a lot in recent weeks after the free agent produced a truly fine performance in his country's 1-0 defeat by Germany at Euro 2016, helping Michael O'Neill's men reach the last-16 stage of the tournament in the end.
It was reported by The Scottish Sun, via BBC Sport, last week that McGovern had rejected a move to Premier League outfit Southampton in the fear that he would play second fiddle to the brilliant Fraser Forster at St Mary's Stadium.
But HITC Sport reported last month that Leeds United were among his suitors, while The Bristol Post claim that Alex Neil - who worked with McGovern at Hamilton - is keen on taking him to Carrow Road as the Canaries look to bounce back into the top flight at the first time of asking.
The report goes on to claim that Wigan Athletic and Bristol City could also be interested too.