Koeman was appointed by former president Josep Maria Bartomeu, and could be on his way out of the club if Laporta decides to put a coach of his choosing on the bench.
"What Koeman is doing is extraordinary, he deserves an opportunity to be part of the new project," Ten Cate told Catalunya Radio.
"He's done a great job, really good, and it's happened a bit like it did with us. He's made the team grow day by day and now it's much better than three months ago."
Ten Cate compared the current situation to that of 2003, when Laporta began his first spell as Barcelona president, and the Dutchman was made assistant coach to Frank Rijkaard.
"We [at Barcelona] also worked with really young players, like Xavi, [Victor] Valdes, [Andres] Iniesta, Gabri, Oleguer and later [Lionel] Messi," Ten Cate continued.
"You have to remember that we had to do without 15 players who were let go.
"[Joan Laporta] is the best because he knows the football world and has a great ability for valuing people," said Ten Cate.
"He always believed in our work, with the support of Johan Cruyff, of course. He was always on our side, he believed in what we were doing, he knew we needed time and he gave it to us."