Puncheon has been in south London since mid-November and is due back at Saints on January 3 but he has fallen out of favour at St Mary's and Lions boss Kenny Jackett has been impressed with his performances.
Puncheon's agent, Tony Finnigan, told the Echo: "He's enjoying it at Millwall because he's getting a chance to play football.
"I'm aware of the interest from Millwall in wanting to turn the loan into a permanent deal.
"He's a south London lad and Kenny Jackett has been an admirer of his for a long time.
"If a deal can be done I hope both clubs get what they want out of it."