In the emotional answerphone message, the soldier - thought to be calling from Afghanistan - tells his girlfriend Samantha how much he loves her and their unborn child, before finally proposing marriage.
The 90-second call was received by 44-year-old mother-of-three Diane Potts, who heard it when she returned to her home in Gateshead, Tyne and Wear, last Thursday.
Mrs Potts said the unnamed soldier did not sound older than 18 and spoke with a Sunderland or Chester-le-Street accent.
Since then the internet, radio and newspapers have been inundated with people trying to trace the young man and his potential bride-to-be. Hundreds of messages have been posted on Twitter and a Facebook page has been created urging either of them to get in touch.
The message begins: "Hi baby, it's me. I am sorry I could not call you last month, but you know what it is like out here. I should be back in three months so we can be together then.
"One of my guys has just been blown up so I feel sad, I really feel sad... Don't ever forget I love you, I love you so much, I love you with all my heart and I was going to ask you, don't answer, obviously you can't answer, but will you marry me?"
Mrs Potts, an alternative therapist, said: "I was a bit shocked at first and I did wonder whether it was genuine. It's not the usual message. But I felt really touched by it. It was just a young guy and it sounded by the contents of the message that he was somewhere on duty somewhere in the world."
She added: "And the fact he used the local area code might mean Samantha comes from up here. But it could be that he's a local lad who has moved away to another part of the country but still speaks with a North East accent."
A British Army spokesman said: "It's a very personal message and he's probably a little embarrassed about what he's done, and about the publicity surrounding it. Knowing soldiers, he'll probably want to avoid any publicity if he can."