The defender admitted that the move looks inevitable, although it remains unclear if the club will negotiate a deal inside the winter transfer market, or have to wait until the summer.
"A lot of strange things must happen to stop me ending up as a Lillestrom player again," Kippe told Romerikes Blad.
"It's LSK I want to go back to. I hope to sort out a deal with them and be released from Liverpool in a week," added the defender, who played for the Canaries from 1997 to 1998.
Liverpool has asked for a fee, but may choose to release the defender - who has six months left on his contract.
"We have informed Liverpool that we have started with negotiations. Hopefully we will sign the contract with Frode on Wednesday or Thursday," said Lillestrom's Bjarne Sognnaes.
"I have faith that this will be sorted out.
"As soon as we have found an agreement with the player, we will work at getting Frode released.
"Until now they [Liverpool] have demanded a transfer fee, and I not sure what will happen if we sign a contract with him.
"We will be very focused on behaving correctly in these negotiations - to not provoke them any more than necessary."