Reports on Wednesday claimed that Forest had bid £400,000 for the 25-year-old winger, who is out of contract at the end of the season.
"We've offered Martyn a new deal but he doesn't want to discuss his future at the moment," Scunthorpe boss Ian Baraclough told BBC Radio Humberside.
"The speculation concerning him is unsettling for not only the player but all concerned."
Woolford joined Scunthorpe from Blue Square Premier club York for an undisclosed fee in 2008.
His finest moment was scoring the winning goal in the League One play-off final in 2009 against Millwall which saw Scunthorpe promoted to the Championship.
Source: PA
Source: PA