The 23-year-old spent last season on loan at Sunderland having struggled to make an impact for Brendan Rodgers' side and was linked with a return to the Stadium of Light, as well as QPR, before the transfer window closed at the end of August.
Borini has made two Premier League appearances so far this season, starting once against West Ham, but his representative revealed that the former Chelsea frontman is determined to battle for a regular place in the side.
"At this moment I am certainly not going to look for another club, as the boy is happy to remain at Liverpool," said De Marchi. "Let's not forget he left a journey he already started at Roma in order to come to England.
"He has managed to find some space playing in the Champions League and starting in the Premier League. Things are progressing as expected.
"Borini is a top-level player, so consequently he has a contract with Liverpool and any club interested knows how to approach them.
"Liverpool have no intention of loaning him out, as they already proved in August.
"The situation is exactly the same as it was in September, in the sense that he is very happy to be part of this important team."
Borini scored 10 goals in all competitions for Sunderland last season, but has yet to open his account for Liverpool in the current campaign.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1