The Duke and Duchess of Sussex reached out directly to the Princess of Wales ... though it's unclear exactly when they tried to make contact or if they actually spoke to Kate or William.

We also don't know if Kate spoke with either Meghan or Harry ... but, we know they made an effort to send their best wishes personally.

It's a sweet gesture from the former senior royals ... who had already put out a statement conveying their sympathies to Kate, William and their children after the princess' shocking revelation.

As we previously reported ... the Sussexes told us, "We wish health and healing for Kate and the family, and hope they are able to do so privately and in peace" just a couple of hours after the announcement.

Meghan & Harry were out at an art exhibition in Los Angeles Thursday night looking pretty relaxed, and reports are surfacing that the news was as shocking to the couple as the rest of the world ... but, it's unclear if they had any advance warning.

Of course, a huge wedge was driven between Meghan, Harry and the rest of the royal family when they decided to step down from their positions and leave for America ... but, it seems this news was bigger than any current personal issues.

This all falls in line with what Sean Mandell -- creator of the "Spilling Royal Tea" podcast -- told us on "TMZ Live" Friday ... when he said this diagnosis may actually be an opportunity for a little royal reconnection.