In March the firm revealed it was in preliminary negotiations that might lead to an offer, boosting its shares. That potential suitor has not been identified.
The company said in a statement: "These discussions have been constructive, however, it has not been possible to reach agreement on the terms of any offer."
Tullett, which acts as a middleman in derivatives trades between investment banks, also said revenue was down 12 per cent to £312m for the four months to April from a year ago.
But the company described its position as “strong”.