The 22-year-old from South Wales, who received a standing ovation from all four judges, has told The Huffington Post UK: "It could be on the cards, I suppose."
The emotional ballad, originally written for the soundtrack of film 'City of Angels', is now back in the charts thanks to Robbie's acoustic performance.
Asked about seeing the song in the top 10 of the iTunes charts, Robbie revealed: "I'm just a normal person who has sung the song and it's been televised. Now one of the greatest songs I've heard has gone straight back to the charts, so it's an awesome feeling to know that I've put it there."
Robbie, who started discovering his voice at about 13 or 14, but hadn't sung in public "at all" until he was 18 when he started performing in pubs and clubs, also told HuffPost UK why he wouldn't have auditioned for BBC rival talent contest 'The Voice' - despite its focus being on singing.
"For me 'The Voice' is good, I watch it, but it's such a new programme I don't actually know what the outcome is for anyone at the end of it," he claimed.
Adding: "I've never seen anyone go in to it and come out the back of it, where as I know people who've been on 'Britain's Got Talent' and are still going now."
Asked what makes him different to every other male singing with a guitar, the unlikely star said: "I like to think I've got quite a stylistic voice and if it was played over radio you would recognise it straight away."
What do you think? Has Robbie got what it takes to win Britain's Got Talent?
All the pictures from Saturday's BGT...