Morrison has been in sparkling form for the Hammers as they build up towards Saturday's Premier League opener against Cardiff at Upton Park.
The 20-year-old netted after just 16 seconds of the 2-1 friendly win over Champions League play-off contenders Pacos de Ferreira on Saturday - his sixth goal of the summer.
Noble has been impressed with his midfield colleague and told the Daily Mail: "He's done brilliantly this pre-season.
"He's not been late, he's turned up to every session, he's trained hard and obviously he's getting the benefits now."
The former England Under-18 international, who has only made one competitive appearance for the Hammers to date, spent the whole of last season on loan at Birmingham in the Championship.