Borini was drafted into Anfield last summer in a big-money switch from Roma, allowing him to work under Rodgers for a second time - having previously enjoyed a productive loan spell at Swansea City.
The Italian forward struggled for form and fitness throughout 2012/13, though, preventing him from making the desired impact.
Further attacking reinforcements have been acquired by Rodgers during the current transfer window, suggesting Borini may find it increasingly difficult to gain recognition.
He is, however, still part of Rodgers' plans and will be given every opportunity to stake a claim for a regular starting berth.
Asked if he had given any thought to sending the 22-year-old out on loan, Rodgers told Liverpool's official website: "Not at this moment in time.
"There would be a queue of clubs wanting to take him if he was available. We want to keep a strong group - it's a very long season for us. You've got Daniel (Sturridge), Fabio, (Iago) Aspas and Luis (Suarez) to come in a number of weeks.
"We want to make sure the competition in the group is there, especially at the top end of the field where if you have a goalscorer it's always good to have."
Pressed on whether Borini had expressed any concern at the added competition for places, Rodgers added: "No, not at all. He's very settled here, he's fighting to improve his performance level. He's doing extra after training with the coaches.
"Any player wants to play games, that's why they become a footballer - to play in the games. He's continued to work hard, he's not just satisfied. He's eager and hungry when that chance comes to prove he can get goals."