I use an alloy with a very low melting temperature to form a low-melting alloy with the solder. One commercial product for that is called ChipQuick. I believe it is mostly bismuth; although, I think almost any low melting alloy will work. If there is gold plating, I have been advised by Indium America not to use an indium-containing solder, as it will remove the gold. That may not be an issue for you. Mercury will do the same thing, but I hope you do not even think of using it.
The process is simple. First, I use desoldering braid to remove excess solder. Then I add an excess of the low melting solder to form an alloy at the joints. Finally, I remove the chip with low heat, like a regular hot air gun focused on the back of the board. That method worked quite well with a QFN accelerometer I needed to remove a few weeks ago. I also add a little paste flux to help the metals flow together better.
John