Postecoglou, who last month quit the national team after clinching FIFA World Cup qualification, is firming as the man to succeed Frenchman Erick Mombaerts with the three-time J.League champions.
An official announcement could come in a matter of days, with the club 20 per cent owned by the City Football Group confident of bringing Postecoglou on board on a multi-year contract.
It's an appointment that would delight Degenek, with Postecoglou responsible for identifying him as a national team talent and handing the 23-year-old all 15 of his caps.
"There's been plenty of talk around the club and in the media in Japan about Ange possibly taking over," said Degenek.
"For me it's an exciting prospect ... I'd be very happy to have him here and to work with him again.
"He gave me my chance to play with the Socceroos.
"And the fact he could be coming here is a boost for me psychologically and also playing wise, because I can learn from somebody like him.
"I know Ange well and I will be the first one to help him out in any way I can if he comes.
"I can help him learn a bit more about the club, the people and the way things are run here.
"I'll give him a heads up in any way I can.
"We'll just have to wait and see what happens.
"I have no concrete knowledge in terms of how close it is ... it's all in the papers here and even my teammates have been asking me questions about Ange."
The departing Mombaerts, who steered Yokohama to a fifth-place finish this season, will be in charge for the last time in Saturday's Emperor's Cup semi-final against Kashiwa Reysol.
He's left a lasting impression on Degenek, who has a year left on his two-season deal.
"I guess he's still here until the run in the cup ends, successfully or otherwise, and he's a very good and positive coach," he said.
"He's been here three years and I learned a fair bit from him in what's personally been a good season for me.
"He's done his bit and he now wants to move on."
Should Postecoglou be confirmed in charge then it will play a significant role in convincing the ambitious utility to commit himself fully to a second season in Japan.
"If Ange comes in then my decision on where I will be next season becomes a bit easier," he added.
"If he comes then I would have to have a chat with him and see what his plans are because I obviously want to be playing and make sure I go to the World Cup next year.
"I don't want to just go as part of the squad ... I aim to go there and play."
Degenek, who would like to see a new Socceroos coach appointed as expeditiously as possible, believes Australia will be competitive in Russia in a group which includes France, Denmark and Peru.
"I have every faith in the team and whoever the new coach is will already have a strong base to build on," he insisted. "I just hope whoever it is understands Australia and the tradition we have and the football we are playing.
"It's disappointing that Ange won't be there leading us but he has his reasons.
"I'm not aware of them and I don't need to know. It doesn't change my opinion of him.
"I respect everybody's decision and I respect Ange and wish him nothing but the best because he deserves it.
"Perhaps our paths will soon cross again."