Sourcing current with sink LED driver
Firstly, these drivers do not sink or source power. The stuff they source or sink is current. Power is the rate of energy use or conversion. Current is the flow of electric charge. Very different things.

The arrangement of LEDs you have is called common cathode, because the cathodes of all the LEDs are connected to the same thing.

A driver designed to sink current can not be made to source current. It's certainly possible to design a driver to source current, but this would be a different component. I took a quick look on TI's web site and didn't find anything equivalent to the driver you were considering, but which sourced current. I'm sure someone makes one, but it's somewhat less common.

I'm guessing this is a hobby project, so you aren't going to incur any unacceptable cost by using a few more components. So, you might consider skipping the driver IC. Here's one way you might do it:







simulate this circuit &ndash; Schematic created using CircuitLab

The transistor bases can run directly to a microcontroller, or an ordinary shift register.