St Mirren have decided not to pursue their interest in former Dundee United midfielder Greg Cameron or ex-Everton and Wycombe man Kevin McLeod.
But former East Fife defender Gordon Gilbert, who has been two seasons with Kaizer Chiefs in South Africa, is still hopeful of winning a deal.
All three have been on trial, but manager Danny Lennon has decided he does not need the two midfielders.
Lennon is looking to strengthen other areas of his squad.
And he said of 22-year-old Cameron, who was released by United at the end of the season: "I spoke to his agent - it was a more specific position we were looking for.
"The boy certainly had the ability, but we feel we are particularly strong in that area."
To win games you have to attack and the game is supposed to be about entertaining
St Mirren manager Danny Lennon
The 29-year-old McLeod had also been looking for a new club after being released by Wycombe following six months there.
He had begun his career with Everton and moved to QPR for £250,000 before spells with Swansea, Colchester and Brighton.
However, Gilbert hopes to be given another chance after being forced to pull out of a closed-doors game against Newcastle on Tuesday with a groin strain.
The 27-year-old started his career with St Johnstone before heading for East Fife, leaving in 2005 for South Africa, where he played for Tuks, MP Black Aces then Kaizer Chiefs, from whom he spent a spell on loan with Moroka Swallows.
Lennon has brought in 10 new players to the club, but he said: "I've still got money in the budget and if I find the right quality comes along to strengthen the squad then we will certainly strengthen it."
Meanwhile, Lennon says simply surviving in the Scottish Premier League is not good enough for him and he wants the Buddies to finish near the top half of the table.
"I always set targets for players and coaching staff and I had a meeting with them and I told them 'if you want to finish second bottom then you're no good to me'," he told BBC Scotland.
The former Cowdenbeath manager is also promising an attacking approach from his team.
''Don't get me wrong, I'm happy to win 1-0," he said. "But to win games you have to attack and the game is supposed to be about entertaining.''
Lennon's Cowdenbeath were promoted to the First Division at the end of last season and he has signed several of that team for the Buddies, but he is confident they are capable of playing in the top flight.
''In training and pre-season, they haven't looked out of place," he added. "We know their strengths - that's why we brought them here.''
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