The music mogul, 60, endured a six-hour emergency operation after falling off his bike at the beginning of August, while trying it out in the grounds of his Malibu mansion.
Simon broke three vertebrae in the fall and had a steel rod inserted in his back.
The father-of-one has been resting at home following the accident last month and has taken time off from all his television appearances, including the Britain's Got Talent semi-finals.
Speaking to hosts Piers Morgan and Susanna Reid on Good Morning Britain on Monday, Amanda said: "According to his partner Lauren he's doing amazingly well.
"He is a workaholic, as we all know.
"He's watching the show and having a lot to do with the edit."
Piers, 55, also brought up the fact that Amanda, 49, had been promoted to head judge while Simon takes some time off.
"I didn't even know about it," Amanda explained.
"It was a lovely surprise."
Referring to Piers' time as a BGT judge, she joked: "I'm just glad it's not you."
Britain's Got Talent has hit the headlines recently after Diversity's politically-charged performance during the show's semi-final attracted over 15,000 complaints.
It saw a man dressed as a police officer kneel on troupe leader Ashley Banjo's neck in a moment that echoed the killing of unarmed black man George Floyd.
Banjo, who is the leader of Diversity, has stepped in as a temporary judge on Britain's Got Talent after Simon injured his back.
Speaking about the performance, Amanda said: "The number of negative complains means this conversation is right.
"What hasn't been highlighted is the hundreds of thousands positive comments."
"Ashley is doing a great job, we stand by him and the performance one hundred per cent."
Piers added: "If you got more of a problem with a Diversity dance over the killing George Floyd then you have a problem."
Amanda finished her chat with Piers and Susanna about discussing her upcoming performance on BGT as well as her debut album.
She said: "The album came from mine and Chris' 10th anniversary.
"I posted a video of me and my girls singing on Twitter and it went nuts and I was offered an album deal.
"Every single song Chris and I chose means something to both of us
"With You, which is out now, includes some emotional lines. It was very much how we felt when we lost our baby boy Theo to stillbirth.
"It's about life love family."
Good Morning Britain airs weekdays on ITV at 6am