But Parkinson is not going to be attempting to bring the 34-year-old to The Valley to help with Charlton's pursuit of League One promotion.
The Addicks boss told the London News Shopper: "I would say no to that because we've got Miguel Llera, Christian Dailly and Sam Sodje.
"There is also young Yado Mambo who is out on loan doing really well and getting better and better, so unless we got injuries in that position it is a no.
"Obviously we lose Sodje for the Barnet and Oldham games on international duty, but there is no need to bring Matt Lawrence in at the moment."
Warnock said regarding interest in Lawrence from other clubs: "We've heard nothing as of yet."
Charlton 2/5, Draw 7/2, Exeter 8/1