The announcement was made by new president Manuel Dominguez Platas, who has been drafted into the role following the resignation of Miguel Guillen on Friday.
A 3-1 victory over Levante in midweek did little to lift the gloom surrounding Betis, who continue to prop up the Primera Division standings and are seven points from safety ahead of Monday's derby with Malaga.
The change in president immediately raised questions over the future of Calderon, who only took the reins in January, but the 54-year-old will remain in his post - for the time being.
"Calderon has a contract for us playing in the first division. If that status changes, Calderon is not contracted for the second division, as that was not foreseen by the club," Platas told a press conference.
"The board has the ultimate responsibility and will make the decision. Or maybe Calderon does not want to be in the Spanish second division. You should talk to him.
"However, I don't want to talk about Betis going down. We will continue to fight to avoid relegation."
Monday's opponents Malaga are not clear of relegation danger either, with a 2-1 midweek defeat against Espanyol leaving them four points above the drop zone.
Defender Vitorino Antunes is hoping their season run-in will pass off as smoothly as possible.
"The most important thing is to maintain our good form away from home. We have to stay in the top flight and do it quietly," he told reporters.
"The derby with Betis will be a tough game, you have to tackle this game like you want to win it. We have to give everything because if we get something positive we can be calm."
Malaga captain Duda is suspended for the trip to Seville while Fernando Tissone is facing a lengthy spell out following surgery on a torn cruciate ligament.