The Scotland international is widely expected to leave Bloomfield Road this summer after the Seasiders' relegation from the Premier League, having excelled in the top flight last season and requested a transfer in January.
A number of clubs tried to sign Adam during the winter and Liverpool are now thought to have resumed their pursuit of the 25-year-old, with talks expected to take place later this week.
Oyston admits there has been contact regarding a possible move but has made it clear that no offers have yet been received.
He 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."