A resolution is expected to be found within the next 24 hours with the Northern Irishman likely to be presented as successor to Kenny Dalglish on Friday.
"I was contacted by Liverpool last night and they expressed their wish to speak to Brendan regarding their vacancy," said Jenkins in a statement on Swansea's official website on Wednesday night.
"I had a discussion with Brendan to talk about their interest and his views on whether he wanted to speak to Liverpool.
"He expressed his wish with me to do that and he has spoken to Liverpool today.
"At the moment we are currently in talks with the owners to agree compensation.
"We are trying to finalise that within the next 24 hours."