Sunderland have already had a £14 million bid accepted, but Borini's desire to stay at Anfield has led to Poyet considering a second loan move for the Italian.
Borini looked as if he was on the move to the Stadium of Light after a bid of £14 million was accepted by the Reds but the Italian seems keen on staying at Anfield and fighting for his place.
His agent has previously commented that the 23-year-old's aim is to stay on Merseyside but a further loan spell in the North East could still mean that Borini's long-term future remains at Liverpool.
The report cites that Borini's desire to play Champions League football is another stumbling block to any permanent move to the Black Cats.
If a deal were to take place, it would leave Liverpool manager Brendan Rodgers looking for two strikers given the move for Loic Remy collapsed. Borini himself is recovering from a shoulder injury he picked up in a pre-season friendly against Roma in Boston last week.
Poyet is clearly keen on landing Borini after his impressive loan spell at the Stadium of Light last term, where his goals proved to be crucial in Sunderland's bid to avoid relegation, along with their run to the League Cup final.
But given the current situation at Liverpool when it comes to their strikers - with Daniel Sturridge and Rickie Lambert their only other recognised players in that position - a different deal to the one that is already on the table could be difficult to agree.
If Sunderland are to eventually get their man, they may have to wait until Liverpool bring in another forward.