The Sun says United have decided on the England U21 international ahead of fellow striker targets Victor Osimhen (Napoli), Benjamin Sesko (RB Leipzig) and Hugo Ekitike (Eintracht Frankfurt).
Delap has scored 12 goals in 30 Premier League appearances for Ipswich this season and will leave Portman Road this summer with the Tractors Boys set to be relegated.
Any deal with United will be benefit local rivals Manchester City, which hold a 20 per cent cut of any sell-on fee. City sold Delap to Ipswich last year for £20m. They also hold a £40m buy-back option, but won't be getting involved in their ex-player's sale.
Delap recently told the East Anglian Daily Times: "I'm so happy here, I'm enjoying it so much here. I just look forward to playing football. I take every game as it comes and focus on the next.
"It (the media speculation) is something that I try to stay away from. People around me have told me to stay away from it, it’s something that I’m very good at, focusing on what I want to do. That’s playing football here."