The Northern Irishman is out of contract after taking charge, on a caretaker basis at first, in late November. At the time, Halifax were 10 points adrift of safety and rooted to the bottom of the National League.
Harvey inspired an immediate improvement in results, but a damaging run of eight defeats in 14 games during Spring ultimately proved the club’s downfall.
Relegation was confirmed on the final day when Guiseley leapfrogged their neighbours.
Asked about his future in the wake of yesterday’s stirring Trophy win, and amid reports that the club may make a move for North Ferriby manager Billy Heath, Harvey said: “My contract was until the end of the season and I don’t know what will happen next.
“I know the chairman (David Bosomworth) is going to announce something on Monday. I hope he is going to announce that he is going to speak to me and offer a new contract. But that is up to him. It is not something I can answer, apart from saying that I hope he does offer it to me. I would love to do the job.
“I have really enjoyed it and I hope he says I can have the job. I would love to correct what has happened with this relegation and put it right.
“The chairman has ambition to get into the Football League. I would love that challenge.”
Yesterday saw a bold step taken by the Football Association as, for the first time, the Vase and Trophy finals were staged on the same afternoon.
In terms of tickets sold, the initiative was a huge success with 46,781 fans coming through the turnstiles. In the Vase final, Morpeth Town hit back from conceding in the second minute to thrash Hereford FC 4-1.
Chris Swailes, the former Rotherham United defender, made history by becoming the oldest player to score in a Wembley final at the age of 45.
The new concept is a worthy one, but yesterday showed the format does need some tweaking.
Setting the two kick-offs four hours apart was a mistake if the aim was to encourage as many fans as possible to watch the final not involving their own club.
By the time Halifax kicked off against Grimsby, for instance, only 250 or so of the 20,000 Hereford fans who had been present for the Vase final were still inside Wembley.
Those who did stick around saw a valiant effort from the Shaymen that Harvey hopes can earn him a crack at bringing the club back up next season.
“This team was dead and buried six months ago,” added Harvey.
“No one was giving them a chance and the supporters had given up on them. In truth, though, we should have avoided relegation. But we got to the Trophy final and won it, that speaks volume for the character of our players.
“This is the first time I have been involved with a team that has been relegated and it is horrible. I gave them a week off to go and lick their wounds.
“But we came back in and things were bright. Fair play to the chairman, he put his hand in his pocket to make things easier for us in terms of preparation.
“We trained at Milton Keynes and then Barnet. We stayed in a nice hotel. It allowed us to ditch the disappointment and focus on the final. The players responded extremely well.
“When I first turned up earlier this season, there was not a lot to feel good about. To turn that around and give those fans a win at Wembley, that is where my satisfaction comes from.
“We have given those people a day to remember. To beat Grimsby, who are going into the Football League, is a massive result.”