Oyston is livid that after six successive defeats to start the campaign, Riga returned to his native Belgium last week rather than focus on improving the fitness of a squad which played just two pre-season games over the summer.
The relationship between the two appears to be nearing an impasse after the transfer window closed on Monday without any more arrivals at Bloomfield Road, despite Riga's claims he needed four more players
And reports then emerged on Saturday that Riga would depart the Fylde coast after a mere 87 days in charge.
In an interview with the Blackpool Gazette on Tuesday, Oyston remained coy on whether Riga would be shown the exit door, but the chairman did stress his fury at the manager's actions over the past week.
"Until I've spoken to Jose personally, I don't want to comment about the speculation or go into it in too much detail," said Oyston.
"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."
Although the Seasiders are rooted to the foot of the Sky Bet Championship table, Riga has been faced with numerous hurdles since assuming the role in June.
There were just six professionals on the books when he arrived and Blackpool did not have a goalkeeper until Joe Lewis joined on loan four days before their season started at Nottingham Forest, where Riga was only able to name four substitutes because players were not registered in time.
Those that did feature evidently lacked match practice as Blackpool played just a pair of pre-season friendlies over the summer, cancelling a trip of Spain to focus on their much-needed recruitment drive.
There were issues going on above Riga's head too
In July, Oyston and club president Valeri Belokon became embroiled in a public spat over the former's apparent reluctance to provide investment to the playing squad - a gripe which many of the club's supporters share.
One man who is likely to sympathise with Riga is former Blackpool striker Michael Chopra, who blasted the club's training facilities when speaking at the Soccerex convention on Monday.
"When I was there the training ground was a disgrace," Chopra told Sky Sports News HQ.
"You were training and trying to do weights and you've got water coming through the ceiling
There's buckets all over the training ground; you can't go to a professional workplace like that and expect to get results."
Source : PA
Source: PA