The 19-year came into his own this past season after having to lead United's attack following a season ending injury to Zlatan Ibrahimovic.
Cole, who scored 121 goals in his six year stint with the Red Devils, was full of praise for the England international.
Speaking to MUTV, Cole said of Rashford: "He keeps learning and keeps progressing,".
"I think the start of the season was tough for him but what I liked about him was he went back to basics.
"How he got into the team was by getting in behind and stretching teams because no team likes players running in behind.
"He's got pace in abundance and, from there, he gets enough space in his feet to run at people and, when he got back in the team, I thought he did really well.
"He is looking more and more like a centre-forward, aiming to get more and more goals, and he has got to be more clinical but that will come with age. He is only a baby. He's learned from some good players, Zlatan and Wayne Rooney, and you've got to learn off players like that. It's about taking bits of their game and adding it to your game so, come next season, he'll be even better for it.