The London businessman has reassured staff that "all payments and wages due to themselves, players and football creditors would be paid in full this week, subject to Conference status".
The Football Conference say they need concrete assurances from the club.
If football creditors are not paid by Saturday's Conference Annual General Meeting, the club risk expulsion.
I want to see the club back in the Football League as soon as possible and I'm confident that we can do that
Conference general manager Dennis Strudwick said they did not want to expel any member club, but had to protect the integrity of the competition.
"We're not here to put clubs out of business, we're here to protect our members," he told BBC Hereford & Worcester.
"We have made it very clear to Hereford what is expected. They have to pay their football creditors and, thereafter, the board will consider its options.
"They have just had a winding-up petition, which has been adjourned, and given them a bit of time, but the debt is still there.
"They then face another winding-up order in a short period of time and have a number of football creditors.
"We need compelling evidence that Hereford United will not only start next season but will finish it."
In the club statement released by Hereford, Agombar, whose son Harry played for both Swindon Town and Macclesfield Town, said: "I'm a football man and I want what is the very best for Hereford United and its supporters.
"They've endured a very hard time in recent months and years. We have to put things in place to avoid that happening again.
Media playback is not supported on this device
"I want to see the club back in the Football League as soon as possible and I'm confident that we can do that.
"We are currently liaising with the Football Conference regarding the club's current situation."
Bulls chairman David Keyte, whose own future is not yet clear, was reported to have been in talks with three different rival bidders regarding a takeover.
A statement was released last Thursday saying that the consortium of investors involved in trying to take over at Edgar Street had "begun the process of payments" to the Bulls' football creditors.
But the club are also overdue with their latest PAYE tax demand and they remain under a winding-up petition brought by former Hereford manager Martin Foyle, which was adjourned on Monday for 28 days.
Tommy Agombar has taken over as owner of financially struggling Conference Premier side Hereford United.