Dublin singer Ryan auditioned for BGT two weeks ago, and received four yeses to make it through to the call-backs later this month.
But the 19-year-old had previously appeared on The Voice of Ireland, making it through to the live shows.
While the teenager was booted out in the first round, he still signed an exclusive contract with Universal Music, which is currently preventing him from going any further on Britain's Got Talent.
It means that unless lawyers can work out an agreement between Universal and Sony Music, the label behind Britain's Got Talent, Ryan will have to withdraw from the show.
Bressie, who picked Ryan for his team on The Voice Ireland, said: "It's an awful shame to hold [Ryan] back, no one will benefit if that happens.
"He has a really good chance on that show, I think he could go far in the UK."
Ryan wowed the BGT judges with his own song, No Name, written for a pal he had a crush on.
Bessie added: "In an ideal world, Ryan could have sang his own stuff on The Voice -- his song was really good and very touching."