Boyle, 48, came in second in last weekend's finale of the TV talent competition.
She was taken by ambulance Sunday night to the Priory Clinic in London where she was voluntarily admitted and is being treated for exhaustion after enduring weeks of unexpected media attention.
"I talked with the Prime Minister last night, and he was very concerned about Susan. He heard what happened and wanted to make sure she was OK," Morgan told "Inside Edition" in an interview that aired Monday.
Judge Amanda Holden confirmed reports Boyle was anxious leading up to the show's finale.
"She didn't sleep. She wasn't eating. I saw her just before she went onstage, they were doing their rehearsals and I arrived," Holden told "Inside Edition." "She told me she felt tired and sick with nerves, and she was worried she was going to be sick."
Boyle's brother, Gerry, told "The Early Show" Tuesday the singer "seems to be coming back to her old ways."
"I mean, she's fine," he said. "She's sounding a bit more like herself ... Eager to come home to Scotland from London, and just, you know, she seems to be on the way back, which is marvelous."
Gerry Boyle went on to say his sister's biggest concern is whether she will have a career after last Saturday's loss.
"Will people still want to hear her sing? And will there be a career for her as we stand here today?" her brother said she was wondering.