Pardew takes Saints to South London on Saturday for the first time since his departure last November, with his former assistant Parkinson having led the Addicks to six straight wins at the top of the League One table.
"We still talk, we've chased the same players which has created a bit of banter between us," said Pardew. "They've got themselves in a great position and I'm pleased for them and the players I left there."
The clash, which as recently as April was a Championship fixture, now sees the two sides at opposite ends of the League One table with the Saints still looking for their first win.
But Pardew added: "I can't change the table but we've got a strong team and will be able to compete with Charlton.
"Charlton and Phil know this division well and he's had time to assemble that side and they look very strong. But we've made good strides as well and I think we'll give them a good game."