Montgomery first saw Drogba in action for Le Mans, ahead of him leaving for Guingamp.
He told talkSPORT: "I went to watch (Florent) Malouda and then big man was on the bench.
"Came on for the first game for 20 minutes and I thought ‘oof’, I went back looking at my files.
"I'd seen him at Le Mans once before and had him noted as a ‘keep an eye on’ and because in them days you had your own database.
"Then I went back to the next game and came on for 30 minutes and then they played Lyon which was the top of the league and I always loved a player at Lyon called Edmilson, who I tried to get to Newcastle with Sam Allardyce later on.
"He was captain of Lyon for four years, then captain of Barcelona for four years and then captain of Brazil.
"He was amazing and I thought I'll go to that game because they're playing Guingamp and they were leading 2-0 at halftime.
"Big man comes off the bench second half, scores one, makes one. I thought ‘oh, aye aye’, and I remember going back and travelling back and when you’re someone like me, if you see something like that, that's different, it's different."
Montgomery also stated he had convinced Drogba to join the Hammers, only for them to be relegated at the end of the 2002/03 season.