The agency commented, "L and Kim Do Yeon became close friends after being acquainted through a mutual friend... However, they are not dating like it has been said."
They further added, "INFINITE, including L, even now, are hard at work on their world tour."
Another rep offered a bit more details as he said, "Kim Do Yeon is one of many friends that L came to know towards the start of their world tour through another friend... From what I know, they are just two among many close friends. They are not a couple."
[Update] - Reps of the agency are now speaking to media outlets over the phone, going more in depth about the situation.
One rep told a media outlet, "INFINITE has been on a world tour starting August. Currently, INFINITE, their managers, and staff are at Bangkok. We weren't able to confirm it with him until later so our official statement was also late... Due to the rehearsals and tour preparations, the members and reps are all very busy...The two are just friends who came to know one another due to another friend. It hasn't been all that long since they've been friends. They're not dating like it's been said."
Another rep said, "Because L was handling schedule overseas, it took us some time to confirm. He said they are just simply friends... He wasn't aware of all the matching clothes and shoes and is quite shocked himself... He met Kim Do Yeon at a gathering with friends, and became close with her along with others." Regarding Kim Do Yeon's tweet, the rep said, "Since Kim Do Yeon is close with L, it seems like she was just expressing her affection also in the point of view as a fan, it doesn't seem like it means anything more than that."
As for the 'Do Yeon' L listed in the 'Thanks To' section of the group's album, one rep said, "We don't know if that Do Yeon is that Do Yeon."