The Colombia international played a key role in helping Udinese qualify for the Champions League next season and has been linked with a move to the Premier League.
The 24-year-old is back in South America preparing with his country for the Copa America, but has revealed he is in talks about leaving the Serie A side and hopes to agree a switch to Anfield.
Asked about his future by La FM, he said: "I do not know what to say, I can say that I am very close to Liverpool. At the end of the Copa America, we will see what happens with my future."
He added: "I have gained experience, but the time has come for me to make the jump to a big team."
Zapata has also attracted interest from Bayern Munich this summer and still has two years left on his Udinese deal, so is likely to cost in the region of £7-10million.