Kishishev is out of the first team frame under Alan Pardew at Charlton and is hoping to get some football under his belt.
The Bulgarian international midfielder joined United at the beginning of March and made his debut against Sheffield Wednesday last week.
Kishishev is already hoping for an extended stay at Leeds, as the Elland Road club bid to avoid dropping into League One.
"Alan Pardew said no pressure, you can stay here. I said I have to go," Kishishev told the club's official website.
"I love playing football and I wanted to come to Leeds to play football.
"I hope to stay longer, but that's not just down to me, because I want to play football and help this club get out of trouble."