The versatile defender is out of contract at the end of the 2012/13 campaign and is currently able to speak to other clubs.
However, the 20-year-old, who can play at full- back or centre-half, has impressed greatly since forcing his way into the first team this season.
And Gers boss Ally McCoist is believed to be keen to keep the hugely promising player at the club for the long haul.
The Northern Ireland Under-21 player's preference will certainly be to remain with his boyhood heroes beyond the summer.
Hegarty was the first player to commit himself to Rangers "newco" last year when he penned a one-year deal. The Dungannon-born kid had gone without wages after his previous contract expired, having received a personal assurance from McCoist he would be offered terms. Hegarty has, along with contemporaries like Fraser Aird, Barrie McKay and Lewis Macleod, been one of the successes of the season for Rangers.
He has started in his team's last 10 games during an 11-match winning run that has seen the Light Blues storm 17 points clear at the top of the Irn-Bru Third Division.
Hegarty had no qualms about pledging his future to the Glasgow club last summer despite months of off-field upheaval and massive uncertainty about the future.
He said: "I said all along I'd come back after the summer ready to play for Rangers and do my bit to help get them win whatever league they play in.
"We are the same club with the same fans and goals we score will be celebrated the same way.
"I'm champing at the bit to show what I can do. This is a big opportunity for the younger guys and the manager has faith in us, which helps.
"Ally McCoist and his management team have been great me and since I joined the first team.
"They've given me the belief that I belong here, I'm grateful to them for the opportunity and will try not to let anyone down.
"It was a summer of uncertainty for me being out of contract. But the manager made it clear I was in his plans and my agent and I agreed to let the club sort out the bigger issues before chapping on the door. Everyone's been good to their word."