Borini struggled greatly at Anfield last season, as he scored just one goal as was clearly not a good fit for Liverpool.
Borini made just 12 Premier League appearance in 2014-15.
The Italian international had previously spent another stint in Liverpool’s first team, before transferring to Sunderland on a loan deal.
He showed more potential in his time with Sunderland, as he scored 10 goals in 40 total appearances.
However, the 24-year-old striker turned down a £14m offer for a permanent deal with Sunderland.
Due to his frustrating time at Liverpool, Borini is more than likely to leave for another club.
The Italian international’s agent, Marco De Marchi, claimed that his client is eager to leave Anfield and felt like a “caged lion” when playing there.
Moyes, who used to manage Liverpool’s arch rivals Manchester United, has admired Borini for a long time.