But Wednesday have also lodged an offer, and hope that their proposed signing of Akpo's brother Sam from Reading - expected to go through this week - will give them the advantage.
"Akpo was a real handful against us in pre-season," Wednesday boss Brian Laws told BBC Radio Sheffield.
"That's what we're missing at the moment - someone who can be a real physical presence for us.
"We're waiting for Vale's response, but we can't increase the bid any further."
Iron boss Nigel Adkins has not admitted to an interest in the player, but has said he is after a tall target man with a physical presence.
Sodje, 27, is in the final year of his contract at Vale Park and the Valiants are likely to cash in now rather than risk losing him on a Bosman transfer next summer.