The Tannadice sporting director was speaking after he introduced new Dundee United manager Jack Ross.
Asghar hopes to be able to offer Ross some extra funds to strengthen his squad with the Neilson issue now expected to go to a SPFL tribunal.
Hearts remain adamant that they are not due to pay a fee for Neilson, who they hailed as being recruited on a “free transfer” from United on their official website earlier this month.
The Tannadice club fiercely dispute this and Asghar believes they have the evidence to prove their case. The issue hinges on the timing of the new deal United offered the 19-year-old defender earlier this year and whether it was made in time to protect their right to training compensation.
“There’s been a lot of talk about Lewis Neilson,” said Asghar. “We have a case that I assume will next go to tribunal. We feel that we’re due compensation as a football club. “That’s with our legal team and the SPFL at present.”
Asked if he was confident of success, Asghar replied: “Very confident.”
Hearts manager Robbie Nielson worked with his namesake while they were at Tannadice together and he is delighted to have tied up his signature at Hearts.
But it remains to be seen whether the Tynecastle club will have to stump up cash for the highly-rated player, who made nine first-team appearances for United last season.