The Scottish international was linked with a move to Boro, after The Teessiders' move for Leeds United's Seth Johnson fell through.
Burley, though, has confirmed he would be staying at Pride Park
"There was the possibility of a move," said Burley.
"But I'm happy to stay here and play in the last 17 games. I've got no problem with that."
Boro are still confident of completing the move for the pair.
"We are very confident that both players will be signed by the 12 o'clock deadline, which means they will be able to play against Newcastle," commented Boro chief executive Keith Lamb.
Meanwhile, Boro's defensive starlet Andrew Davies has been named in Wales Under-20 squad.
