The new all-female 'W Series' is looking to become a support event at grands prix.
The single seater series kicked off at the weekend as a support for the German touring car series DTM.
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But David Coulthard, a leading figure behind the W Series, said organisers of the Australian grand prix wanted to host the women in March.
"I was really excited," the former F1 driver told reporters at Hockenheim.
"The team was just, at that stage, (saying) 'If we don't get it right for whatever reason'... And they made the right decision," Coulthard admitted.
But he thinks it is possible the W Series will be at the grands prix before long.
"I think it would be quite interesting if there was a little bit of pressure applied to F1," said Coulthard.
"I think it fits perfectly with the new owners (Liberty Media) and everything they stand for and what they are doing. We have had a conversation, they would like to see how it develops."