"I wish her all the very best. I can't wait to meet her," Kate, who's married to Prince William, said. "We haven't met her yet. I hope that will be soon."
ET has learned that it's been Kate who's been serving as an "intermediary helping to smooth relationships between Harry and the royal family," following Harry and Meghan's bombshell interview with Oprah Winfrey which aired in March.
A source notes that Kate, with whom Harry has always been exceptionally close with, realizes the importance of maintaining William and Harry's brotherly bond.
The source also says that Kate is doing whatever is necessary to be a "peacemaker" between Harry and other hurt relatives, adding that Harry "texted with Kate after Lili’s birth."
Royal expert Katie Nicholl previously told ET that the royals hope "that this little baby is going to be a rift healer."
"This family division has really gone on for a long time now, well over a year," Nicholl said. "It has been many, many months since [Prince] Charles and Queen [Elizabeth II] and the Cambridges have seen Archie in the flesh. We know that there has been some really quite deep problems between Harry and William, difficulties between Harry and his father and I think that it is everyone's hope that this little baby will be a peace offering in many ways and that she will hope to bring this divided family back together."