The Swans are on the lookout for a successor to Brendan Rodgers, who left the Liberty Stadium for Liverpool last week.
The Premier League side were believed to have approached the Tangerines for permission to speak to Holloway regarding the vacant managerial position at the Welsh club.
However, Swansea chairman Huw Jenkins is currently out of the country and Oyston has confirmed they are yet to receive any contact from the Swans.
"I know it's manager silly season at the moment but we've not had a call from anyone enquiring about taking Ian as manager," Oyston told BBC Sport.
"[That] amazes me, I have to say, after what he has done here, what he has worked with and the way he has gone about things.
"I would think that would make him a prime candidate for other clubs to consider.
"However, surprisingly, and I am very pleased about it, we have not had any calls and I hope that continues."
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