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 a 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.