"Anywhere else within football, you would be totally shocked. But, the way Leeds are at the moment, especially with the owner, nothing surprises you."
It is a growing trend under Cellino's control. Four bosses have worked under the Italian since his purchase of the Championship club was ratified in April, yet none have lasted more than six matches.
Forty-six-year-old Milanic, who was a surprise appointment late last month, is the latest to have been handed his P45 - news which has resulted in Leeds legend Johnny Giles having urged Cellino to sell the club.
However, considering that the 58-year-old entrepreneur swooped in to save the three-time champions of England when they were on the brink of entering administration for a second time, Parker has told Sports Mole that Cellino's departure may not be the most beneficial of outcomes.
"You've just got to look at his track record - it shows you that he's very trigger happy. If you do not do well at the club, he's shown that he's going to have no hesitation in getting rid of you," said the left-back, now of Conference North side Guiseley. "However, you've got to take everything into perspective. When he took over the club, it was on the verge of going into administration again.
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"In that aspect, he has saved the club. You've got to look at it from both sides because he has done well for the club, but at the moment, there is a bit of uproar with the way that he is treating the managers. There is no stability, but maybe he should be given a little more time to see where he can take the club. Without Cellino coming in, the club was in dire straits under the previous owners."
Although the appointment is yet to have been rubber-stamped, Cellino has confirmed that Neil Redfearn is to succeed Milanic on a permanent basis.
The 49-year-old, who has been involved with the youth setup at Leeds since 2009, was placed in caretaker charge following the August dismissal of Dave Hockaday. Under his guidance, the Whites collected 10 points from a possible 12, yet he was overlooked for the job as Milanic took the reins.
During his seven-year professional stint with Leeds, Parker worked alongside Redfearn and he believes that the ex-Barnsley midfielder has already proven that he is capable of getting the type of results and performances out of the players that is demanded by the controversial owner.
"Everyone knows that if you do not get good results almost straightaway, Cellino is likely to sack you. His record in England and Italy is crazy! That's where [Leeds] are, though. Yet, he seems to like Redders, who appears to get how Cellino works, but there has got to be some sort of mutual agreement between the pair, such as saying that Redders gets until the end of the season and then they go from there. A successful club needs stability," stressed Parker.
"Redders is a familiar face - the players know him. The players can relate to him and also trust him. Redders is quite a simple guy - a Yorkshireman. He doesn't try to complicate tactics or anything like that. He likes his players to go out and express themselves with some good passing and creating chances. He also demands that you work hard, so it's a good balance. He's a top man. Players like playing for him. He was with the reserves for a few months when I was there and I played a few games under him. He puts no pressure on your shoulders.
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"As a manager, you've got to get the players to buy into what you are trying to implement and he should already have that following the rapport that he built up with them during his time in caretaker charge. It gives him a good platform to start from. If he gets the job, I expect that he will go back to basics by making training enjoyable and players will want to win for him.
"Trust is a big thing. You look at all the successful teams that have won trophies and earned promotion, there is big trust between the coaching team and the players. Leeds have got a good squad, but some senior players have not been playing and if the manager hasn't been communicating why, that can have a negative impact on the whole squad. If Redders can get that together, which looking from the outside, he managed to do as caretaker, the team should pick up some good results."
Looking ahead, Redfearn's likely first official match as manager will be a trip to Cardiff City - a side that Leeds have not defeated since 1984. That is followed by back to back home encounters against Charlton Athletic and Blackpool, where Parker feels that the Leeds faithful will show their support to the new man.
"I don't think we've won at Cardiff for around 30 years, so it's a difficult start, but if we can go there and maybe pick up a draw, before going back to Elland Road for those two games, the ground should be buzzing," he revealed.
"Most fans wanted Redders before Milanic, so from that point of view, they will be looking forward to getting back to seeing the team play well, which they were doing under Redders. Those are two winnable fixtures."