Kate meets with young children at the Emirates Arena Leisure Centre in Scotland
Tim Rooke/REX USA
04/04/2013 AT 03:30 PM EDT
04/04/2013 AT 10:30 AM EDT
On a visit to Scotland Thursday, the Duchess of Cambridge
gave another hint as to when the world will greet the royal baby.
Kate told onlooker Rachel Sawyer that she is due "around mid-July, but apparently babies have their own agenda."
Whether the little one makes his or her entrance on time, "We have a short list for both [boy and girl names] but it's very difficult," Kate said. "My friends keep texting me names."
Accompanying Prince William
on the visit to Glasgow, the royal (known in Scotland by the title Countess of Strathearn) charmed her audience of well-wishers and future athletes as – in her second trimester – she kept herself and her bump warm and protected against the chilly Scottish wind.
Sawyer also asked when the mom-to-be would be able to put her feet up and relax. Replied Kate
: "around June time."
Wearing high-heel, knee-high black suede boots and a blue-and-gray-plaid dress coat from the boutique Moloh (that cost £425), the couple first stopped at the new Emirates Arena, which will be the flagship venue for the 2014 Commonwealth Games.
Inside, on their private tour of the courts and the Sir Chris Hoy Velodrome, the sporty couple watched riders keep pace on the tracks and saw demonstrations of badminton and netball. Kate also watched – and later chatted with – young children who were running and jumping small hurdles and playing a variation of jumping jacks.
The couple also watched an energetic dance led by the tartan-clad green Commonwealth mascot, designed by local schoolgirl Beth Gilmour, before they unveiled a plaque for the Commonwealth Games.
As Kate and William were departing, a young red-headed girl wearing a Princess Merida costume from Disney-Pixar's Brave
held up a burgundy carnation.
William asked, "Is that for me?" The girl shook her head no. Taking it all in stride, he then said, "It's for Kate. Quite right."
The little girl, who was successful in giving Kate the flower, also turned down a kiss from Prince William.