The Italian has had a stuttered start to his career at Anfield since moving from Roma in the summer transfer window for a reported £10.5m fee.
A broken foot and dislocated shoulder, which he suffered in February, has limited the 22-year-old to just 16 appearances in all competitions this season.
Borini wrote on Twitter: "Who i should be and who I feel to be" today first full training after injury!!! #be #firstraining #back #happy"
The former Chelsea forward has netted just one goal since signing for the Merseyside outfit.