I've taken a couple of Aleve a couple of times while on Tasigna and didn't have any issues. And according to the two drug interaction websites I checked, they both show no interactions between Aleve and Tasigna. So, that tells me it is ok to take both at the same time. Although I try my best to only take Tasigna by itself, and then any other medications a couple of hours afterward.
Hopefully I'm not steering you wrong, so hopefully someone else with a bit more knowledge will chime in.
Here are the two drug interaction sites I checked: