Former Boston boss Greene, 56, was appointed in an interim role at the beginning of October following Gavin Cowan's dismissal.
The club then revealed a fortnight later Greene would remain in charge for the foreseeable future. Greene said at the time the position was permanent, but chairman Andy Pryce said in a fans forum the following week the club remained on the lookout.
Greene, whose side host leaders AFC Fylde today, says he is keen to have further talks with Pryce this weekend to clear up the 'semi-permanent' role he currently occupies. He insists that the position means it is difficult to attract permanent transfers to help improve the club's position of 20th in National League North.
"There's things that have got to be discussed between me and the chairman this weekend," Greene said.
"I'm still 'semi-permanent', so to speak, I went from interim to semi-permanent, the goalposts change all the time.
"Because if I'm bringing in permanent players and then he gets a manager in in a couple of weeks time it might not be beneficial to the new manager.
"Bringing permanent players in has been a bit of a struggle because of the position the club's in.
"We just need to get that sorted out one way or the other, either they are going to look for a new manager, or they're going to stick with me until the end of the season and that way we can start getting some permanent additions in.
"It's changed twice, I was interim for a few games, it was a case of steadying the ship, a couple of loans in areas needed i.e. the midfield.
"But now it's semi-permanent, you want to start building your own team so if you do well you'll be kept on as permanent.
"The more your hands are tied the less you can do the job properly. I think it does need addressing, I've had a chat with the chairman and hopefully we'll get that sorted sooner than later."
Greene is keen to remain in charge at the New Bucks Head but, after two defeats on the spin, the club are keeping their options open.
"Of course I want to be manager," he added. "I feel I can be a success given time, finding permanent players isn't easy at this stage of the season.
"We're fortunate only one goes down, even with the squad we've got I don't think we'll be one of them, and we'll only get better as the weeks and months go on. We've got to build correctly."