Stoke have been trying to offload Beattie since the end of the season and newspaper reports have suggested that they have been pushing the player in Blackburn’s direction.
But speaking to the Evening Sentinel, Allardyce said he has not made an approach to Stoke.
“We have no interest in them at the moment and we haven’t made any inquiries.
“I am surprised to see the stories in that respect, although teams get linked with everyone at this time of year so I suppose I shouldn’t be too surprised.”