An unnamed League One club - not believed to be the Iron - bid an initial £350,000 for the 23-year-old former Bristol City forward, with a further £50,000 paid if the club concerned won promotion.
However, Gillespie still has two years left on his Whaddon Road contract and the club are under no pressure to sell.
"We want to keep our best players if we can. While it's pleasing to receive such interest in one of our players it's the board's firm intention to retain and improve upon the quality of the playing squad," said Baker.
"We want to build upon the success of the last two seasons and to establish ourselves as a League One club.
"We're doing that by keeping our best players like Steven Gillespie and signing new ones like Alex Russell."