Alsa by default uses the same sampling rate and format as the source. It is however possible to force the sample rate up (or down).
Here is one way you could do it. (in /etc/asound.conf or ~/.asoundrc)
Then just make that pcm a slave to another one, like your default(stereo) pcm
(warning: the 24 bit format won't work unless you have a compatible card, I normally use S32_LE which works on most cards.)
the above will however only work for stereo sources (so if you play from a 5.1 source that will by default use the surround51 pcm, things get a bit more complicated)
The one way I know (and personally use) about how to force the sample rate of non-stereo sources is taking parts from this asound.conf/asoundrc(dead link) and modifying them. (Note: I did not write that file myself)
(You can find my asound.conf in this question and just copy that directly instead of going through the hassle of manually modifying it below below)
First copy the "dmixed" pcm, and modify it's hardware section to the desired sample rate and format.
Then copy the !default, surround40 and surround51 pcms from it as they are. This will effectively dmix all output and upconvert the sample rate of all 2.0, 4.0 and 5.1 sources to the sample rate that was set in the dmixed pcm.
In that configuration file you may also find the "upmix20_51" pcm interesting as it is an effictive way to upmix 2.0 sources to 5.1 by selectively duplicating the sounds to the other channels. If you want to use it you will have to change the type of it from "plug" to "route" and then set it as a slave to the default pcm.
As "surround51" which that pcm uses uses "dmixed" as a slave, the forced sample rate will apply to this pcm as well.
Sadly with the way things are now, mono sources will only output from the left speaker, but that is hardly a problem as mono sound sources are rare these dadys. The example I just gave would be exactly how I have my own asound.conf configured, enjoy if you have a 5.1 speaker setup and want to force 96khz sample rates.
In theory I would think that forcing up the sample rate won't achieve anything for you (as it is an absurd thought that it would improve the quality of the audio from it's source which had a lower sample rate) as such you will be a lot better off configuring the application to use 96khz output.
But for me I had some problems with crackling sounds (in specific games, like Xcom: Enemy Unknown) if I didn't force either 96khz or 44.1khz frequency. Seeing as I don't lose anything at all from forcing 96khz (it neither increases nor decreses quality of 44.1/48khz sources) it was a perfect solution.