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."
Source: PA
Source: PA