The 25-year-old Scot bagged 16 goals in Blackpool's promotion season, including a great goal against Yeovil in the Play-Off Final at Wembley. He previously played for St Johnstone, where he scored 30 goals in 90 games for the Scottish outfit.
Reds boss Simon Davey commented to www.barnsleyfc.co.uk about Parker:
"I have seen the things in the newspapers and it is just speculation. I have spoken to a lot of players and clubs this week.
"We do not comment on speculation and we will announce any new players when the deals are signed and completed".
Meanwhile, German full-back Dominik Werling's future at Oakwell is back in the balance after Davey told the Official Site that an offer was still on the table for the Roberto Carlos lookalike.
"To be honest I have no idea where Dominik is. We will have to see whether he turns up at another club this month.
"We have made an offer and that is still on the table. I have not had a letter or anything saying that offer has been turned down although how long it will remain in place is up to question.
"We will have to wait and see and it is up to Dominik and his agent to get back in touch".