United have had a new €35m offer for the young Dane rejected by Lecce, says the Daily Mail.
Lecce are willing to do business this month, but will not budge from their €40m valuation for Dorgu.
United's director of football negotiations Matt Hargreaves was in Italy this week, where he met with agents Frank Trimboli and Leon Angel, along with Lecce president Saverio Sticchi Damiani.
Sticchi Damiani has since revealed: "The meeting was cordial and went well. For us, sitting down at the table with Manchester United to talk about a player who comes from our Primavera is a satisfaction, it means that the club's growth path is notable.
"We explained to them that our desire at the moment is to keep the team unchanged, keeping all the big names, Dorgu in particular. We made it clear that for us this year is an important appointment with history, we could achieve the third historic salvation.
"Although we are flattered by their offer, the priority for us is the sporting result."