Costa said negotiations over Portuguese international Moutinho and Colombia's Rodriguez started after Porto clinched their third consecutive league title on Sunday.
"I only got the news that there was interest on Sunday. We are negotiating," he said in an interview with Portuguese television RTP. He did not confirm media reports that a deal could be worth up to 70 million euros (£60 million).
Monaco, who were bought last season by Russian oligarch Dmitry Rybolovlev, were promoted to Ligue 1 this season.
They are also expected to secure a deal for Atletico Madrid's wildly prolific striker Falcao.