Given my limited knowledge of Japanese, I can only give you the gist of the conversation. This shouldn't be taken as a literal translation.
[youtube=425,350]URBxe0Oj4wE[/youtube]
Sayu: Today is Uta! Doki Talk Day! Yay!
Sayu: Our guest is Konno Asami!
Konno: Hi, nice to be here.
Konno: Sayu! <3
Sayu: Konno-san! <3
Sign: Buddies?
Sayu: For Uta! Doki featuring Konno Asami, how many songs did you sing?
Konno: Solo, I sang 5 songs, and--
Sayu: That's singing too much!
Sayu: That's really singing too much!
Sayu: Anyways, I sang one song on Uta! Doki.
Konno: Oh?
Sayu: Ja-jan!
Konno: Ja-jan.
Sign: Wha?
Sayu: This famous song...
Konno: So there isn't a second or third song?
Sayu: Er, there isn't. Would you like to see Michishige Sayumi in "Jaa Ne"?
Konno: I'd like to see it!
Sayu: Amazing... I love Konno-san. Let's watch it!
Sign: Flattery. (not sure about this part)
While watching the video
Sayu: v-u-den's Erika-chan and Yui-chan
Konno: v-u-den's really nice.
Sayu: Yeah.
After the video
Konno: That was cute. <3
Sayu: Haa.
Konno: It was cute. Sayu was cute, as always.
Sign: More flattery. (Again not sure)
Some stuff said here I didn't catch
Konno: I was really excited about singing on Uta! Doki, so I practiced here and there whenever I could.
Sayu: Like where?
Konno: Like I went to karaoke, practiced in the car. I was glad to do it, even though I had to work at it a bit.
Start of Mirai He talk, some stuff I didn't quite catch
Sayu: I was really moved.
Konno: No way! You really are a good girl, Sayu.
Some more stuff I didn't catch, then talking about songs Konno would like to sing. She says she even likes to sing songs by guys, like B'z.
Konno: I also like Kudo Shizuka! I also like (someone's name I don't recognize)!
Sayu: So it appears...
Sign: So it appears.
Konno & Sayu: Bye-bye
End
So yeah. Not a literal translation, but there you have it.