The 22-year-old held talks with Swansea chairman Huw Jenkins on yesterday and will meet with new boss Michael Laudrup later on today.
New Liverpool boss Brendan Rodgers is confident they can proceed quickly to complete the deal for a player he previously managed at his former club.
The Irishman admitted last month: "He is a very talented player, which everyone knows."
The two Premier League clubs have been in negotiations for over a month with Swansea rejecting the Reds opening bid of £12.5m and Jonjo Shelvey on a season long loan.
Source: DSG