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It comes amid a shutdown of the Super Rugby season due to the coronavirus outbreak.
Rodda, fullback Isaac Lucas and lock Harry Hockings were stood down following discussions with the players and their agent, the Brisbane-based Reds said on Monday.
The Reds said the players were "unwilling" to take salary reductions and be nominated for the federal government’s JobKeeper programme, which is paying workers $1500 a fortnight if furloughed by their employers due to COVID-19.
"Unfortunately, we have had to take the decision to stand down three of our players," Queensland Rugby Union Chief Executive David Hanham said in a media release.
"Given the recent negotiated player-payment reduction agreement, this was not a situation the QRU had expected to face."
The players union and Rugby Australia agreed last month to an interim pay deal, which had players taking average pay-cuts of 60% up until the end of September.
The three Reds players' agent was unable to provide immediate comment.
Rugby Australia's Director of Rugby Scott Johnson said the governing body wanted the players to stay in Australia and honour their contracts.
"We are aware they are looking at their legal position, but we hope this can be resolved with the players as soon as possible and we will keep an open dialogue with them," Johnson said.
Super Rugby was suspended in March after travel curbs and border controls implemented to contain COVID-19 made the mainly southern hemisphere competition untenable.
Under heavy financial pressure, Rugby Australia hopes to follow New Zealand's lead by staging a domestic tournament featuring the country's four Super Rugby sides to generate revenue.