The Italian striker, who has fallen behind Luis Suarez, Daniel Sturridge and Iago Aspas in the pecking order, completed his switch to the Stadium of Light on deadline day.
"It's just to get games," Rodgers told the club's official website. "He had a stop-start season last year with his injuries and I just felt this year he needed to go and play football.
"We had a host of clubs wanting to take him, but with Sunderland having the Italian connection there and being a big club where he can go and play, I'm sure he'll get the chance to shine and we'll look closely at his development this year."
The Reds may have let Borini leave, but the Merseyside outfit brought in defenders Tiago Ilori and Mamadou Sakho on long-term contracts as well as Victor Moses from Chelsea on a season-long loan deal.