Rory Loy looks set to remain with Falkirk after the Bairns rejected a second bid for the striker.
Hamilton, who had an initial £25,000 offer turned down earlier this month, returned to the table with another attempt to secure the striker which again failed to met the Bairns valuation of Loy, whose deal expires in the summer.
No further bids are expected for the ex-Rangers and St Mirren player, nor any of his team-mates.
The Bairns are intent on retaining his services to make progress in the Scottish Cup which continues this Saturday, and also push on into the play-off positions.
A club source told Heraldsport: “The offer was derisory – the money we are looking for to take Rory away at this stage is not going to be paid.
“The bid does not reflect his worth to the team, especially when he has the capability to score the goals that could take us on a run in the Scottish Cup and up a position in the league.
“The cash difference between one place in the league and a cup run compared to the money offered doesn’t justify a sale at all.”
Falkirk don’t anticipate any further bids for any of the players despite scouts keeping tabs on Will Vaulks and Craig Sibbald throughout the season.