Malaga coach Manuel Pellegrini has been linked with the manager's post at City for some time but he confirmed there is still no done deal between himself and the Barclays Premier League club.
However Al Mubarak has now set a timeframe for the new appointment and the criteria the club is looking for ahead of next season's bid to regain the league title.
"We obviously want sustainable success for this club and (picking the manager) is absolutely the most important decision for a football club," Mubarak told mcfc.co.uk in an interview released on Friday but recorded on Monday, following City's 5-3 win over Chelsea in New York.
"The type of person we would like running our football team is someone with great man-management capability and the ability to get the best out of the talent we have, get the best out of the youth we have and establish and continue a systematic approach from the youth team to the elite team and reserves.
"We have a wonderful team running this process internally (to select a new manager) and are putting a very comprehensive process in place.
"They have created a shortlist of managers who fit that criteria and we are pretty much done. We are very close. I expect to make an appointment probably in the next two weeks."
Whether the man to fit the role will be Pellegrini remains to be seen after the 59-year-old Chilean spoke earlier this week of having a "verbal commitment" with the Blues.
He stressed, though, that no contract had been signed, something he reiterated at a press conference where he was previewing Malaga's Primera Division final-day away clash with champions Barcelona on Saturday - a game he has already announced will be his last with the Andalusian club.
Asked if he had reached an agreement with City, Pellegrini said: "Not yet. Next Monday we will see where I go.
"On Sunday I finish my contract here with Malaga and on Monday we will start to see where I go next season."
Al Mubarak was clear with his reasons for wanting a new man in the City dugout after a mostly frustrating season.
"We all felt it was time for a change," he said.
"Our expectations were to come in and achieve more and move forward.
"I don't think we have achieved that this year and that is why we have to re-focus this summer on getting us back on track and again to winning ways. We are a club that has been designed to win Championships. We are here to win, to play beautiful football
"Roberto has done a great job for the club and everybody associated with Manchester City should be deeply appreciative of everything Roberto has done for this club.
"He's won us the FA Cup in 2011 and the Premier League, the Charity Shield. It's been a wonderful ride and Roberto has done an incredible job.
"I have the highest regard for Roberto as a coach, as a manager and as a friend and he will always be someone I will deeply regard as a good friend and a manager.
"But it was time for City for a change. We need something new. We need a change of direction and a decision was made that it was time to part ways.
"I wish Roberto all the best. He's a good manager and I will always be a friend for Roberto but it's time now to look at the new season, to prepare for the new season and to bring in a new manager for the club to continue this journey we have started and hopefully to take us to a whole new level."