Mel has yet to meet the Baggies players and Pochettino hopes his former mentor is a success at the Hawthorns.
"I know him so well that he was actually my teacher, my professor, when I was getting my pro licence at the Spanish FA about six or seven years ago," he said after Saints' 1-0 win.
"I hope that he does well, I wish him all the best. I hope he is able to develop the playing style and I wish him all the best.
"I hope he is able to adapt quite quickly, to establish things quite quickly.
"I hope he is also lucky to find the great and amazing group of players that I have found here, the great staff I have found here, the amazing environment. That has made it a lot easier to adapt to this league."