The Lancashire side have lost all six of their competitive matches under the stewardship of Riga, who took the reins at Bloomfield Road in the close-season.
Riga's short tenure has been beset with problems, with the club's struggle to recruit players during the transfer window leading to a frosty relationship between the manager and Oyston.
Blackpool chief Oyston has also been irked by Riga's decision to return to his native Belgium during the international break without notification.
"Until I've spoken to Jose personally, I don't want to comment about the speculation or go into it in too much detail," Oyston told the Blackpool Gazette.
"However, I have to say I find myself slightly bemused yet again by the actions of our manager.
"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."
