The Giants met with the out-of-contract midfielder on Thursday and gave him a tour of the club's headquarters, but released a statement on Friday saying they would not pursue the talented midfielder.
Just an hour later, the Saints also said they would not be targeting Martin.
“We are approaching the upcoming trade and draft period with a view to strategically building several aspects of our list but Dustin is not a part of any plans we have in place,” Saints list manager Chris Pelchen told the club's website.
Martin is considering his options on the open market after contract negotiations stalled with the Tigers.
Giants football manager Graeme Allan said on Friday the fledgling club had decided against making a play for the 22-year-old.
“We took up the invitation to meet with Martin and his manager Ralph Carr and showed them around our new training facility and Skoda Stadium but we have made a decision not to pursue further discussions,” Allan said in a club-issued statement.
“We will continue to explore a number of opportunities with other players with a view to add more experience to our playing list and we wish Dustin Martin all the best for his career ahead.”
Earlier, incoming Giants coach Leon Cameron said the acquisition of Martin could complete "the jigsaw" of the expansion club's young list.
"He's a very good young lad; a respectful young lad and it was good to meet him, but like anything there will be a number of other clubs looking at him as well," Cameron told Fox Sport News on Friday morning.
"We'll have our best-laid plans at the Giants of who we would like to acquire at our footy club, but 17 other clubs will be doing the same thing, so it's sort of like trying to find the players that fit the jigsaw."
After two years of grooming some of the best young talent in the country on its list, Cameron said Greater Western Sydney needed to start earning respect with its performances in 2014.
"There's no doubt we need to improve dramatically," he said.
"Our first few years were all about bringing in some young talent through the draft and developing them and retaining them which we have.
Martin suitors thinning fast
"But it is important for us, it is important our young group and it's important for our members that we push forward and be more competitive on game day."
Cameron said the Giants remained interested in securing Hawthorn forward Lance Franklin, but would wait until his finals commitments finished before talking to the star Hawk.
"I think Lance has been true to his word; he wants to make a decision at the end of the year and we have seen that through the whole year and that remains the same," he said.
"He's a terrific player and as I have said openly before we are looking at all uncontracted players or players possibly looking for a move."
"It's not a matter of getting the big signings, I think it's just a matter of getting the players from other football clubs that can help our performance on-field."