A Melbourne woman who received a life-saving kidney transplant after police found her in her home and rushed her to hospital says she has "a lot to be thankful for".

The Royal Melbourne Hospital was desperately trying to contact Levalda Adams earlier this month after finding a matching kidney donor.

Ms Adams had been on the waiting list for a kidney for 19 months.

Head of transplants at the hospital, Dr Peter Hughes, said the doctor in charge on the day had tried to call her a number of times.

"We don't have much time once the kidney's available for the transplant to go ahead, usually we have about half an hour to try to contact someone and make sure they're OK," he said.

He said when the doctor could not reach her, she called local police to do a welfare check at her Brunswick West home.

"I believe [the police officers] were also unable to contact Levalda, so there was no sign that she was there initially," he said.

Ms Adams said she was inside the house at the time and could hear the police officers knocking on the door.

"On the day, I was very confused, I had a hypoglycaemic attack in my sleep that night, I heard the knocking on my door, but I couldn't respond because I was out in front of my bed," she said.

"But the police knocked and knocked and knocked and knocked."

She said her neighbour heard the knocking and called her mobile, which she was able to reach from her position and answer.

"I said, I'm coming but I can't walk, so he told the police, and I crawled to the front door and managed to open the door, the police came in and told me what [was] happening," she said.

"I was soaking wet because the fluid from the machine had leaked all over me, they had to put a new nightie on me, they did that in two seconds, and I was out the door."

The two police officers, Senior Constable Dean Turner and First Constable Thomas O'Dwyer, carried Ms Adams out to the car because it was quicker than calling an ambulance.

"As soon as she opened the front door and found out there was a kidney coming, [she] instantly sort of had a bit of energy, because she was excited about the kidney," Senior Constable Turner said.

Ms Adams said the police officers stayed with her until she went into theatre.

"I will be eternally grateful to them, they were fantastic - really, really fantastic," she said.

First Constable O'Dwyer said the "strange" job was touch and go at the beginning.

"We really wanted to find out where she was, even if she wasn't home just to know, and let her know that the kidney was waiting for her," he said.

"We were getting calls from the hospital and they said half an hour, and we were looking at our watches and time was running out a bit."

Kidney transplant recipient now recovering well

Ms Adams is now recovering well.

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"We're a few weeks down the track now and Levalda's out of hospital and doing extremely well," Dr Hughes said.

"I think the police have just shown incredible caring and commitment to Levalda to achieve this and I think they saved her on that day, and I think they've allowed her to have a transplant that she wouldn't have otherwise received."

Ms Adams said she had expected to wait for a kidney for another three years.

"The kidney was a big surprise to me, I thought that I would wait much longer," she said.

She thanked the nurses and doctors at the Royal Melbourne Hospital, who she said were "fantastic" and the family of the organ donor.

"I would like to say to the family that I am very grateful for what they've done for me, they've really saved my life, and with everything else, I have a lot to be thankful for," she said.

Senior Constable Turner said it was "jobs like these that keep you [going], they're the good ones".