Dover chairman Jim Parmenter would not reveal the value of the bid but said he did not take long to reject it.
"You can't really call it a bid," he told BBC Radio Kent. "It wouldn't buy a Ryman South player - it's one nought away from where we need to be."
Earlier this week Parmenter, who said he was unaware of Gillingham's bid until he heard it broadcast on
BBC Radio Kent
, had said he would not stand in Birchall's way if a satisfactory bid came in for him from a football league club, but said he would only join Gillingham "over my dead body".
However, he appeared to leave the door open slightly for Gillingham on Friday morning, adding: "Everything has its price. If the offer was something we couldn't refuse we would have to consider that position.
"But I see no prospect of Adam joining Gillingham."
Parmenter confirmed that the bid is the only offer the Blue Square Bet South club have received for Birchall from a league club.
Birchall, who had a transfer request rejected last week, was brought to Dover in 2009 by Andy Hessenthaler, the current Gillingham manager, after being released from Barnet by Ian Hendon, now the Gills' assistant boss.
Source: BBC Sport
Source: BBC Sport