San Francisco general manager Brian Sabean, director of player personnel Bobby Evans and John Barr, Sabean's special assistant, denied the report, though Sabean said negotiations with Gillaspie were "further along than the other" unsigned players the Giants drafted in the first four rounds.
With the Aug. 15 signing deadline less than two weeks away, none of San Francisco's top four selections has inked an official deal.
Buster Posey, the Giants' first pick and the fifth overall selection, is one of seven top-10 picks who've yet to sign. Of the 16 players in the supplemental round, though, Gillaspie, the 37th pick, is one of only two who haven't come to terms.
The Wichita report said Gillaspie flew to Arizona on Monday morning -- presumably to the Giants' Minor League complex -- to sign his deal.
"As you get into the last 10 days [before the deadline], little rumors like that creep up," Evans said. "We're working hard to sign everybody now, but nothing with Gillaspie is done."
Per club protocol, Evans wouldn't discuss the details surrounding negotiations with any of the top picks. The Giants won't publicly discuss the signing process because "details about one situation could bother kids who are dealing with a different situation."
Among third-round selections, Roger Kieschnick, the Giants' third pick and the 82nd overall choice, is one of only three unsigned players. Brandon Crawford, the Giants' fourth pick, is one of just six unsigned players in the fourth round.
"I know Bobby has been having a lot of discussions with all of those guys," Barr said. "We're working on finalizing all those guys."
A third baseman for Wichita State last season, Gillaspie batted .419 with a .697 slugging percentage and 92 RBIs in 60 games.
The deal Gillaspie is rumored to have signed falls in place with his draft-slot value. The player chosen directly ahead of him, Kansas City's Mike Montgomery, negotiated a $988,000 signing bonus June 17.
The Houston Astros chose Jordan Lyles directly after Gillaspie, and his signing bonus was just shy of $1 million.
David Biderman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.