Can you find malaria parasites in saliva?
No.
Although malaria is transmitted through the saliva of a female Anopheles mosquito, it stays in the bloodstream and doesn't pass over to the saliva of humans (otherwise it probably would be transmittable via humans directly). Once the parasites travel to the liver, it infects and bursts hepatocytes after reproducing (asexually). The burst cells then infect the bloodstream via red blood cells, where the parasites reproduce further and eventually burst their host cell, leading to a vicious cycle. This whole process only has to do with the bloodstream, since the parasites live in red blood cells.  

However, there are certain markers present in the saliva which can be used to detect the presence of malaria the most known of which is called PfHRP2, or Plasmodium falciparum histadine-rich protein 2. This only applies to people infected by the type of parasite P. falciparum, however it is this parasite type which is the cause for the vast overwhelming majority of deaths and complications during malaria infection. The range of PfHRP2 values in malaria-positive patients' saliva ranged from 17 to 1167 pg/mL in one study.  

References:  


http://www.malariajournal.com/content/11/1/175
http://www.jstor.org/discover/10.2307/30086299?uid=3738432&amp;uid=2&amp;uid=4&amp;sid=21104875852967