Gallacher needs to finish in the top two to dislodge Irishman Graeme McDowell from the final automatic qualifying place in Paul McGinley's European team for Gleneagles.
The 39-year-old kept his hopes alive with a 69 yesterday to head into the final round in Turin in sixth place, four shots behind Ramsay in second and six behind leader Hennie Otto.
Austria's Bernd Wiesberger lies third on 13 under after following consecutive rounds of 66 with a 71, with English duo Lee Slattery and Ross Fisher sharing fourth on 11 under.
"I would hate to be the person to deny him a place on the Ryder Cup but I know if it comes down to it, he plays to win and that's the same attitude I have to have," said Ramsay, who holed from 40 feet for birdie on the 18th to complete a flawless 66.
"Stevie is a fantastic player as he has shown to get into contention. He will perform on Sunday and I wish him the best in getting the Ryder Cup place, but I have to accomplish my job of getting into the mix and picking up win number three."
Ramsay, who won the South African Open in 2010 and European Masters in 2012, added: "It's a tough one because I know Stevie well. It's a big, big ask for him, but he has shown how good a player he is and if he did not qualify automatically he would be an asset to the team, not only because of his ball-striking but his attitude as well. His record at Gleneagles is impressive too."
European captain Paul McGinley missed the cut in Turin, but stayed to watch the final two rounds ahead of naming his three wild cards at Wentworth on Tuesday.
Gallacher has said all week he just wanted to be in with a chance today and achieved that thanks to a round containing four birdies and one bogey. "It keeps me in touching distance," Gallacher said.
"The worst thing I could have done was open up a big gap, which was insurmountable. I've not done that so it's all to play for. You never know what happens in this game, guys have won from further back than this. I'll just try to get as many birdies as possible and see what happens.
"This is the only time in my career that I would be happy not to win a golf tournament. Second will do me fine on Sunday."
Italy's Francesco Molinari has not given up hope of claiming a second Italian Open to boost his chances of a Ryder Cup wild card, a third-round 69 leaving him one behind Gallacher on nine under.
"I holed a good putt on the last so maybe that's a sign of things to come tomorrow," the Turin native said. "You need to hole the putts and I haven't done that all week so I'm looking forward to doing that tomorrow."
Otto began the day with a three-shot lead after a stunning 62 on Friday, but struggled to a 71 in just his second tournament back after two back operations.
"It was a rough day," said the 38-year-old, who carded five birdies, two bogeys and a double-bogey seven on the ninth. "My back started to tighten after eight holes, but I managed to get round even though I couldn't swing it properly. It's uncomfortable but not painful enough to stop me playing.
"I'm not worried about it. I was in serious pain before the operations, but this is nothing like that and I can get it fixed with stretching and physio."