Sandoval, who is scheduled to become a free agent after this season, reportedly declined the Giants' three-year, $40 million offer last month.
Sabean, speaking Tuesday in an interview with Yahoo! Sportstalk Live, said the Giants are "probably at the end of the rope" in their negotiations with Sandoval.
"We've given our best shot with good faith intended to try to get him signed, and they've drawn a line in the sand that we're not going to beat nor should we meet," Sabean said. "Things have been tabled and we'll see what happens up the line, but we're not going to have ongoing talks from this time forward."
Sabean did not rule out the possibility of reaching a deal with Sandoval at some point this season, but said that the seven-year veteran would have to perform to the level of the contract he is seeking.
"Anything's possible," Sabean said. "I just don't know how probable it is, because right now Pablo is pretty much going to have to play to get to the [salary] number that they think he's going to be able to command on the open market.
"We disagree that he's going to get that number, per se, from the Giants on the open market."
Sandoval, 27, is a career .296 hitter and a two-time All-Star. The switch hitter was a key contributor to San Francisco's two recent championship squads and was named the MVP of the 2012 World Series, when he tied a record with three home runs in Game 1.
Sandoval has spent his entire career with the Giants, but Sabean reiterated that the team is not willing to meet his asking price. Fox Sports recently reported that Sandoval was seeking a five-year deal.
Sandoval has gotten off to a slow start this season, batting .161 over his first eight games.
"At this point, the organization has put its best foot forward and [Sandoval's agents] have decided it's not to their liking, and we understand that and that's the reason it needs to be tabled," Sabean said. "He needs to concentrate on baseball right now.
"I think he might be pressing a little bit because it's in his head one way or the other. But now it's definitely been shut down, at least for the time being. I think he needs to get on with baseball."