The Denmark international was the subject of an offer from United of €25 million (£21 million) last week, which was turned down.
United are ready to try again with a bid closer to €35m (£29.5m) for Dorgu.
Transfer expert Ben Jacobs is reporting: "Manchester United are optimistic a deal can be reached with Lecce for Patrick Dorgu for under €40m.
"Club-to-club negotiations continued today. Napoli not to be discounted, but Dorgu keen on a move to Old Trafford."