The 25-year-old, who had a loan spell in the Premier League with Blackpool last season, is surplus to requirements at St Mary's.
His agent, Tony Finnigan, has confirmed Pompey have made an enquiry and that Puncheon would consider signing for the Blues.
"Southampton don't want him there. They want to sell him, so people are being encouraged to enquire," Finnigan told The News. "He is a good player but [Southampton manager] Nigel Adkins doesn't want him. He has gone from playing at Old Trafford to playing with the Under-16s.
"Portsmouth have made an enquiry to find out what the price would be and there was a chat. Jason is a good player and just down the road from them so I'm sure they would have seen him a few times.
"Of course he would be interested, he is not wanted by Southampton so needs to go. I don't know the price Southampton have put on him or what they are going to do. It is out of my hands."