Borini was originally not due to join his new club until August 1.
Reds boss Brendan Rodgers told liverpoolfc.com: "Fabio will come out next week with the England players, and that's a great demonstration of his commitment to Liverpool.
"He was involved with Italy right the way through to the (Euro 2012) final and I'd given him the time off, like the others - four weeks.
"He was due to come back on August 1 but he made it very clear when he came that he wanted to get back and train with the group.
"We've agreed that he'll come out next week and we're looking forward to seeing him.
"He is very determined and committed to doing well and I'm sure he'll play some part in some of the games once he's over here."