Ambrose has been strongly linked with a move to Championship rivals Queens Park Rangers.
The 26-year-old signed a new three-year contract with Crystal Palace in the summer.
Burley is keen for goalkeeper Julian Speroni and midfielder Neil Danns to also sign new deals with the club.
“Darren is going nowhere,” said Burley. “There was a lot of speculation in the summer when we worked very hard to keep him.
“He agreed to sign a three-year contract and he is very happy to stay.
“He means a lot to us. I brought him up as a kid at Ipswich and gave him his debut when he was 17.
“He makes a lot of difference to us. He has quality, assurance on the ball, is always likely to score a goal and is an excellent professional.
“The board are determined to keep hold of our best players. I am hopeful we can also keep Julian and Neil – even though they are out of contract. They are important to us.”
