The South African forward was released by the Whites at the end of last season, with persistent knee problems forcing Brian McDermott's hand.
Somma has, however, been allowed to use Leeds' training facilities as he works his way back from a third operation.
The 28-year-old is now closing on a return to full fitness and clinging to the dream of landing fresh terms at the Championship outfit.
Somma told the Yorkshire Evening Post: "I definitely feel like I've got unfinished business at Leeds.
"It's hard to know what's going to happen and the gaffer's going to make his own decisions, but when he spoke to me in the summer he said I could come back, get myself fit and then let the club take a look at me.
"He wasn't in a position to offer me a contract there and then, which I understood. He wasn't going to give me a contract when I wasn't fit. But I'm a month away from being fit enough to train properly and if I'm able to do a bit of training with the first team, then I'll do my best to impress."
Somma who netted 12 times in the 2010/11 campaign as he managed to steer clear of the treatment table, added: "I never thought I'd be two years down the line and still trying to get myself right.
"It's been tough but I always wanted to get back playing and I always hoped to make more of an impact at Leeds.
"If there was a chance for me, then I'd take it with both hands."