The pair, who worked together at AS Monaco, were involved in friendly exchange in the wake of the Saints' 2-0 win in the quarter-finals, and Puel opened up about the embrace in his post-match interview.
"Arsene just told me to go on and win it," The Guardian quotes the Southampton boss as saying in response to question about Wenger's remarks.
Addressing his side's performance, Puel added: "We were clinical in that half, two chances and two goals, and I like this.
"We actually created many more chances in the second half and could have made the game safe, but it was still a fantastic result for us. Good solidarity, good attitude... I enjoyed what my players did."
Southampton will take on Liverpool over two legs in the semi-finals of the tournament.