Koeman will bring his Everton side to St Mary's for what will be his first return to the club since leaving to take over at Goodison Park in the summer.
The Dutchman enjoyed two successful seasons on the south coast, guiding Saints to respective seventh and sixth-place finishes in the Premier League.
Puel, who succeeded the 53-year-old as Southampton manager, wants the club's supporters to hand their former boss a warm welcome.
"I think he did very good at Southampton last season, to get the players to be able to (qualify) for playing European games. I have a lot of respect for his work," Puel said at a press conference.
"Of course it should be a positive reaction for the players to see their former trainers. For the fans it is important to respect also all of his work here and to now be behind their team."
Despite his respect for Koeman, Puel insists his side's main focus remains securing all three points.
He added: "Now it is the most important thing to just consider this game, which is against a strong (Everton) team, and not just against a former trainer."