After his side began the season with five consecutive Championship defeats, Riga returned to his native Belgium last week rather than focus on improving the fitness of a Tangerines squad which played just two pre-season friendlies.
Oyston has admitted that while he is unhappy with Riga's actions, he has not decided if he will part company with the 57-year-old.
"Until I've spoken to Jose personally, I don't want to comment about the speculation or go into it in too much detail. However, I have to say I find myself slightly bemused yet again by the actions of our manager," Oyston told the Blackpool Gazette.
"He has said, on many occasions on the record, that he would use the international break to get the players up to fitness and to work with the squad we now have. The first thing the manager does is hop on a plane and clear off to Belgium for a week without telling anyone.
"Let's face it, we've lost every competitive game he's managed and these actions aren't the most professional way to get us out of this position. To hop on a plane without telling your employer or your colleagues isn't right. It's something I will be speaking to him about."