Despite Spurs' form collapse in the Premier League, Murphy can't see a change being made midseason.
He explained to Tribalfootball.com: "I do think they'll leave it until the end of the season.
"They'll know a lot more in the next couple of weeks in regard to the FA Cup and League Cup of course, but the Europa League is a massive deal.
"If they were to win that, and they are one of the favourites, then they could be in Europe that way.
"So, if they were to win that, it makes things a lot better.
"I don't think changing managers in February or March time, if things don't go well over the next month or two, is going to have a positive impact on the team.
"I think it takes a manager a while to implement ideas, and somebody's going to want to bring their own players in.
"I just don't see the logic in getting rid, there's not a standout candidate everybody's desperate to bring through the door or whose sitting in the wings.
"Sometimes there's somebody on the side lines, if I think back to Liverpool when Roy Hodgson was struggling, and Kenny Dalglish was in the stands.
"The Liverpool fans wanted Kenny back in and that's what happened.
"Tottenham doesn’t have that situation, so I think he will stay, and I think he should stay and be judged at the end of the season.
"But it is a really precarious position for him at the moment, it's a massive couple of games coming up in those two cup competitions."
On reports of some players are now complaining about Postecoglou's tactics and training methods, Murphy believes it won't be concerning the manager.
He continued: "Since the day I played football, there's always players who are going to be disgruntled, agitated, frustrated, moany or whingy about the manager.
"Even when managers are successful, the players who aren't playing are still having a whinge.
"I think more often in the more recent years these kinds of things get out more than they did in the past with social media and all the different ways that people talk now.
"I think Daniel Levy will stick with him, as I've said before, I don't see the benefit in getting rid.
"There's not a perfect person to come in and in the summer, if they were to get rid of Ange, there's going to be many more options than they'd have now.
"So, I don't think it's helpful if players are leaking disgruntlement about their situation or the training because it just keeps more pressure on the players as well as the manager.
"You don't want that when you play, you want to be an environment where you try and get the supporters back on board, and everyone is it together.
"It's just the way the world is at the moment with footballers and not just footballers, but people now in life generally do a lot of chatting about everything online and things get leaked.
"But I do think he'll stick with him, and I hope he does.
"I don't think a few disgruntled players is new, it's just part and parcel of a situation when results don't go so well, players and start questioning things.
"We were all moaners; football players are all moaners.
"We all think we know better than the manager, and I used to. I used to whinge more than anyone, go and see the manager about this and that.
"It just didn't get out as much back then, but I don't think Ange would be too worried about a few players whingeing."
- Danny Murphy was speaking to Tribalfootball on behalf of Betway