I'ts a transformer, but it's not neccessarily the cuprit itself even if it's making the noise.
If it was quiet when it was new then I'd say it's certainly not a problem with the transformer, but rather one of the electrolytic capacitors in the regulator circuitry concerning that transformer. They can have dried out, destabilising the regulation.
Look for bulging tops and isolation retreating away from the top. Small cap's (like the size of the two in front) around the control IC or in hot spots are especially suspect.
