The Italian has been sidelined since dislocating his shoulder during the Anfield side's 5-0 win over Swansea City in February.
The Reds' manager told the Liverpool Echo: "Fabio should also be involved in the squad so we have options. He's recovered really well and is looking very sharp.
"It's been a difficult first season for Fabio. With the injuries he's had it's not been ideal but it's been a great learning season for him.
"If he can help us now over the coming weeks it will give him a platform to build on for next season."
It had initially been thought that Borini would miss the remainder of the season after sustaining the injury.