The 26-year-old defender returned to training last week after 10 months out of action with a ruptured cruciate ligament.
The former Scotland Under-21 cap suffered the injury during an indoor training session but is now ready to return to John McGlynn's squad.
However, Hamill insists he is still not fully match-fit and will not risk his recovery by speeding up his rehabilitation just to try to win a place in the Tynecastle team that will take on St Mirren in the Hampden decider on March 17.
The former Kilmarnock man told HeartsTV: "I would like to be back before the cup final but at this moment in time, I'm not focusing on that. I'm just trying to get back into the swing of things. From there, if I can make it a game or two before the final or a game or two after, then so be it.
"I'm not really pushing myself for the final as such. Obviously it would be great because I missed the Scottish Cup final last year, which was difficult to take. But worse things have happened to me in my life. Hopefully I will make it but if I don't, I'll take it with a pinch of salt."
Hamill feared the worst after he was struck down by the knee injury last April. He suffered both physical and mental scars during the recovery period but is now delighted to be nearing his return.
"It's good to get back in the atmosphere of being around the boys," he said.
"I'm happy and the physio is happy to let me off the leash. It's taken a lot of hard work through the 10 months I was injured. It's been difficult mentally for me. When I first got injured I thought I would never play again. The gym work is relatively easy but it's tough mentally. It's just about getting your head around being out for so long.
"I was expecting it to be six, seven months (out) but we hit a few snags along the way. That's difficult to take but there's no point rushing back and doing yourself harm."