The two men offered the guard 50,000 kronor ($7,350) to look the other way, the local Arbetarbladet newspaper reports.
According to the guard, referred to only as Mats, the two men wanted to kidnap the goat using a helicopter and take it away to Stureplan in central Stockholm.
The recent kidnapping plot can be found among a number of incidents recorded by Mats and his colleagues charged with ensuring that the towering straw goat survives until Christmas.
The erecting of the Gävle goat, a tradition which dates back to 1966, takes place on the first Sunday of Advent in the town's central square, Slottstorget.
And while building the goat, which has measured as high as 13 metres, has become one of the town's most cherished Yuletide traditions, attempting to burn it down before Christmas is almost as popular.
Last year, the goat was torched in the early hours of December 23rd, while in 2008, it survived through Christmas, only to go up in flames on December 27th.
In order to protect the goat this year, the town hired a security firm to watch over Gävle's holiday treasure. So far, the measure has succeeded in keeping the goat free of flames.
“If the goat were to burn on my shift, I'd never be able to show my face in town again,” Mats told the newspaper.