The news of the invitation has increased speculation that the 16-year-old may be named as the youngest winner of the Nobel peace prize later this week.
The Queen has been very impressed by her bravery and also asked Pakistan's high commissioner to the UK, Wajid Shamsul Hasan, about her recovery, the 'Sunday Times' reported on Sunday.
Malala had been airlifted to Birmingham for life-saving surgery after being shot in the head and neck by Taliban gunmen for speaking out in favour of girls' education.
Malala has given her first detailed account to the British newspaper of what happened when she was shot on the way home from school in Pakistan a year ago.
The teenage activist revealed her terror at coming out of a coma at Queen Elizabeth Hospital in Birmingham six days later with no idea where she was.
"I was terrified. Where were my parents? Who had brought me there?" she said, in reference to her four operations in Britain and crediting the surgeons for giving her "a second life".
Malala, who now lives and goes to school in Birmingham, will be in the US this week to launch her memoirs, 'I Am Malala', of her journey from schoolgirl to educational activist taking on the Taliban.
Her message that all children be allowed to go to school have made her a favourite to win the Nobel prize, to be announced on Friday.
Her memoirs are published worldwide on Tuesday, in which she has also chosen to name and thank Fiona Reynolds, an intensive care specialist at Birmingham Children's Hospital who was visiting Pakistan when the young campaigner was critically wounded last year.
Reynolds had her moved to an army cardiology hospital with better intensive care and stayed with her alongside a team of nurses from Birmingham.
The 47-year-old also had the tough task of informing Malala about what had happened to her when she came around in the Birmingham hospital.
"I didn't know what had happened. The nurses weren't telling me anything. Even my name. Was I still Malala? No one told me what was going on or who had brought me to the hospital," recalled Malala.
She then became so worried about the cost of her treatment that she thought of sneaking out of hospital to get a job.
"I thought, 'I need to go out and start working to earn money,'" she said.
The attack on her also wounded two other girls but to Malala's frustration the only person in custody is the school bus driver, who is being held in case he needs to identify a suspect. "Why do they arrest him and not the Taliban leader," she asked.