The two are close acquaintances.
Broadcasting star Yoo Jae Suk recently talked about his current dynamic with actor Song Joong Ki.

In the June 28 episode of Yoo’s YouTube show Pinggyego, Song Joong Ki’s name was brought up by Lee Hyori, who was the guest of the show.

During their conversation, Lee mentioned her previous collaborations with Song on a show and mentioned that he had recently appeared on a radio program hosted by her husband, Lee Sang Soon.
In response, Yoo Jae Suk expressed his regret that Song Joong Ki had not yet appeared on Pinggyego, jokingly asking Lee Hyori to help arrange an appearance.
The host then honestly admitted that despite his close friendship with Song, they have not kept in touch as much as before, because Yoo felt “awkward” to contact him given his current situation.
We used to contact each other from time to time, but after his marriage and everything, it feels a bit awkward to contact him.
— Yoo Jae Suk
Yoo explained that now that Song Joong Ki is married and raising to children, his life has changed completely, which makes him hesitant to interrupt.
Song Joong Ki confirmed his relationship with Katy Louise Saunders at the end of 2022 and they tied the knot just a month later. The couple welcomed their first child in June 2023 and their second child in November 2024.

You can read more about the actor’s married life here:
Actor Song Joong Ki Tells All About His Married Dad Life In Italy