If the royal baby is born in April it will share a birthday with Prince Louis, who was born on April 23, or even possibly the Queen who was born on April 21.
During their visit to Birkenhead the Duke and Duchess visited Hamilton Square where they inspected a new statue that marks the 100th anniversary of English poet and soldier Wilfred Owen's death.
The couple's walkabout was their first since their Pacific tour and they met the public, chatting and shaking hands, while Meghan received flowers.
Excited fans shouted "Meghan" as the royal pair unveiled a plaque, before they met local veterans and members of the Birkenhead Institute Old Boys, which Owen belonged to.
Harry gave a four-year-old in the crowd a hug after seeing her sign that said 'Gingers Unite - I love you Harry'.
"I love this, do you love your hair, this sign is amazing," he told the little girl.
They will also visit a number of community organisations including Tomorrow's Women Wirral, an organisation that supports women in vulnerable circumstances.
Meghan has been a vocal supporter of women's rights for several years, from the time she first shot to stardom as an actress on Suits.
Last week it was announced Meghan would become patron of Smart Works, which helps long-term unemployed and vulnerable women get back into employment, helping with interview coaching and mentoring, and providing work-ready clothing for them.
Animal lover Meghan will also become patron of Mayhew, a historic charity which teaches animal welfare and responsible pet ownership for young people, works to keep homeless people and their dogs together, and runs a pet refuge to care for pets when their owners are in crisis.
She also inherited patronages of the National Theatre and the Association of Commonwealth Universities from the Queen.
"The Duchess is delighted to become Patron of both national and grassroots organisations that are part of the fabric of the UK, and is very much looking forward to working with them to bring wider public attention to their causes,'' Kensington Palace said in a statement.
"Her Royal Highness feels she can use her position to focus attention on, and make a particular difference to these organisations and, more widely, the sectors they each represent.
Meghan has indicated she intends to work until late in her pregnancy.