Carrick has won four times in his first four games in charge, though remains contracted to the end of the season.
Neville insists he's been told that no decision on the long-term position will be made until the summer.
He said on his Gary Neville Podcast: "I made my position clear a few weeks ago and what I'm not going to do is repeat it every week, but what I did, I actually spoke to the club, because ultimately the club get asked all the time from journalists and broadcasters, what's the position of the club.
"It's a very difficult situation, you've got a massive movement now with what's happened towards giving Carrick the job, saying that really he should be considered. That's only going to build the more that he wins and the more that he gets closer to Champions League football.
"I asked the club what is the official position of the football club in terms of what you're saying publicly to everybody else. I have to say I thought their answer was pretty good. They said they've actually begun the process now, starting to look for another manager, which I thought right.
"That's good to hear because you need to plan for everything. They've started the process of speaking to and looking at other managers, building all the sorts of data and analysing who should be the next manager of the football club. But what they've said is they're not going to be bounced into - irrespective of wins or draws or losses on the pitch in this next couple of months - making an appointment. They're going to wait until towards the end of the season."
Neville continued: "If Michael then at that point makes himself available for the job, and I did actually say a couple of weeks ago, I wondered whether Michael actually would say no. He is that type of guy Michael, he's someone who would always work in the best interest of the football club. He may do that, or he might say no, I feel comfortable enough and I've built such a good relationship with the players, his coaching staff to put his name in the hat.
"At that point Michael Carrick, like in any other recruitment role in the country for any other business, would go into what would be a process versus the likes of Thomas Tuchel and all the others that are going to become available in the summer. I think that's fair."