Assistant boss Iffy Onuora has taken charge on a caretaker basis, and oversaw Tuesday's 1-0 loss to DOncaster.
Carson told PA Sport: "When a side like Swindon sacks its manager there are always plenty of applications. They keep coming in, they're flooding in.
''But at this stage we don't know, things are up in the air. There's nothing wrong with Iffy, he did a good job with the youth team.
"If he does a good job he might be someone we look at, we're still very open-minded at this stage.''
Former Robins chief executive Mark Devlin has returned to the County Ground as associate deputy chairman.