The Sun says United are not planning on rewarding Greenwood with a new deal after his first-team breakthrough.
Greenwood, 17, made four appearances for United last term and started against Cardiff on the final day.
Ole Gunnar Solskjaer admitted the teenager was United's 'best player by a mile' in the 2-0 defeat at Old Trafford.
Greenwood could become a regular in the first-team next term but United will make him wait before offering a new contract.
The striker is not 18 until October and the Red Devils are eager to learn from previous mistakes with younger players.