Ibrahimovic arrived from French champions Paris Saint-Germain on a free transfer in the off-season and the Swedish veteran has made a seamless transition, scoring 26 goals in all competitions.
Koeman was in charge of the Dutch giants when Ibrahimovic was making his way in football and the Everton manager recalled his time with the towering striker.
"I'm not surprised [of his impact in the Premier League] because he's really that talented and strong," said Koeman. "And maybe mentally he's one of the strongest players what I know. I still admire the boy.
"I know him really well and he is still showing really well at his age being still so important for the team and scoring goals, showing he's still one of the best - I have great respect for him.
"I managed Zlatan when he was young and sometimes also difficult! But, okay, that is normal. I'm also better now to handle for a coach than when I was 19!
"He was funny but we had a lot of young players. [Rafael] Van der Vaart, [Nigel] De Jong, [John] Heitinga, Mido, Zlatan; really big talents at that time, but all were 19, driving Porsches, driving Ferraris!
"I met Zlatan three or four times in the last four or five months. If we speak about that time at Ajax, he knows perfectly how he was when he was 19 and how he is now."
Everton are seventh in the Premier League, three points behind fifth-placed United.