The Scotland international requested a transfer in January and is now expected to make a swift return to the Premiership as clubs begin to circle.
Oyston told the Blackpool Gazette: "We've had a few discussions this summer but nothing conclusive so really there is nothing to report.
"Are the reports wide of the mark? I'm sure that football clubs have talks with lots of players all summer that they probably shouldn't do.
"I'm sure that goes on. If January is anything to go by that is certainly the case.
"It is always difficult (when speculation starts)."
Asked to confirm Liverpool had made contact, he replied: "We've had a few very preliminary discussions and enquiries but nothing of any substance so there really is nothing to report at this stage about interest from anyone."