Pools boss Neale Cooper has been in contact with administrators Wilson Field, but Darlington manager David Hodgson said no offer has been received.
Two other bids have been received for the six-goal striker. Sheffield Wednesday offered to take on Concol on a month's loan, while
Macclesfield Town had a bid of £35,000 rejected.
David Hodgson said: "I've spoken to Baz and he wants to stay and see this through.
"We'll address his situation in the summer but all he wants to do at the moment is help this club. He is a player we need at the moment.
"The offers were not acceptable, and more importantly, we're not really in a position to replace a player like Baz.
"The administrators have left the decision-making to me and in my eyes it would not be right to let Baz go."
Barry Conlon was one of the Darlington players in town on Saturday packing bags in Marks & Spencers before going into the town's center with a "Save Darlo - Crisis Fund" bucket.
Hodgson, meanwhile, has revealed that he will be terminating two unnamed players' contracts.
The Quakers boss is keen to keep their identities confidential until a few details regarding their release have been agreed with the PFA.
"Both lads have been fantastic about it which is nice to see in today's game," said Hodgson.
"It's not often you get players agreeing to leave even when the club is in such difficult circumstances.
"But they are prepared to take a risk and help the football club.
"We are still in discussions with the PFA but the players have accepted our circumstances."