She said: "Having these kids has transformed him from a very miserable person into a fairly miserable person. It's improved him. He's gone up the scale."
MailOnline has contacted Hugh and Elizabeth's representatives for comment.
In January, Anna's mother Susanne is said to have spoken to Swedish tabloid Aftonbladet, to confirm the news as she said: "I'm very happy to be getting another grandchild. She's due rather soon."
Hugh and Anna have two young children together - a son John, born in 2012, and a second child, born in December 2015.
Clearly delighted at the prospect of becoming a grandmother once again, Susanne reportedly spilled the beans to the magazine.
The name of the couple's second child still remains a mystery, but back in 2015 the birth was confirmed by Anna's mother to a Swedish newspaper.
In the statement released at the time, she said: "Anna Eberstein from Sundsvall has had her second child with film star Hugh Grant. The newest member of the family saw the light of day for the first time last Wednesday."
Her mother, a judge and prominent left-wing politician, confirmed to Swedish newspaper Örnsköldsviks Allehanda the baby, her second grandchild, was born.
She went on: "I can confirm that I have another grandchild. It is wonderful that we now have grandchildren (more than one grandchild)."
A close friend of the family told MailOnline at the time: "I heard from Anna's parents that she had given birth last Wednesday. It was a little girl. Everything seemed to have gone okay."
Hugh also has two other children - a daughter Tabitha, six, and son Felix, four, with Chinese beauty Tinglan Hong.
The Notting Hill star went from having no children to being a father of four in just four years.
At the time of Tabitha's birth, Hugh's spokesman said: "He and the mother had a fleeting affair and while this was not planned, Hugh could not be happier or more supportive. He and the mother have discussed everything and are on friendly terms."
When Ms Hong gave birth to Felix, Mr Grant wrote on Twitter: "In answer to some journos. Am thrilled my daughter now has a brother. Adore them both to an uncool degree. They have a fab mum."
In 2014, he spoke for the first time about his son. Speaking to Swedish newspaper Nöjesbladet, he said of Anna: "We are very good friends and she's a very good mother."
The actor said he had plenty of contact with his son. He said: "'I see him all the time, all the time - most days". His relationship with the boy was 'excellent', he said, adding: "I love him very much." He also spoke warmly about the charms of Sweden, which he has visited several times.
Elizabeth and Hugh's close friendship will come as a surprise to many, given that he famously solicited the services of Divine Brown in Hollywood's notorious Sunset Strip in 1995, when he and Elizabeth were still very much in a relationship.
Both the Four Weddings actor and the prostitute were pulled over by the police and detained - leading to Hugh's famous sheepish mugshot.
Liz and Hugh, who began dating in 1987, were plagued with troubles after his cheating was exposed.
The couple worked through their issues, but eventually split amicably in 2000 after 13 years of dating, with Liz previously telling MailOnline that Hugh is 'family' to her.
The pair met in 1987 when Hugh played Lord Byron in a Spanish production called Remando Al Viento, and Elizabeth was cast in a supporting role as Byron's former lover Claire Clairmont. Liz and Hugh, who began dating in 1987, were plagued with troubles after his cheating was exposed.
The couple worked through their issues, but eventually split amicably in 2000 after 13 years of dating, with Liz previously telling MailOnline that Hugh is 'family' to her.
Hugh's children
1987-2000 - Hugh enjoyed an extremely high-profile romance with Elizabeth before splitting following his infidelities. While they never had children, he is Godfather to her son Damian, 15
September 2011 - Hugh became a father for the first time, to a daughter Tabitha with receptionist Tinglan Hong, after 'a fleeting affair'
September 2012 - The actor later became a father for a second time to John Mungo, his first baby with Anna
December 2012 - After a brief reunion, Hugh and Tinglan had another child, as she gave birth to a boy called Felix although this only became publicly known when a birth certificate leaked when he was 16-months-old
December 2015 - Anna and Hugh became parents once more to a second child, although they have never announced the child's name
