Lawrence spent three months on loan at Cardiff last season, and although a deal looks likely, manager Malky Mackay has refused to confirm his interest in the player.
Mackay told BBC Radio Solent: "Liam came in and did a fantastic job for me last season in the period he was at the club. He is a really good character.
"We've got targets that we want to bring into the club, but I can't say whether Liam is one of them."
The 30-year-old is one of two players remaining at Portsmouth as the club look to clear their wage bill to try to avoid liquidation.