The Bayern Munich director and former Germany international says the president of FIFA does not meet the credentials required to run the global game.
Rummenigge, speaking exclusively to Sky Sports News HD in his role as the head of the European Club Assocation, also believes the international calendar is unfair on the clubs and needs to be revised.
But even though he is not convinced Blatter is the right man for the role, he denied there are plans in place to form a breakaway league that would take more than 200 of Europe's top teams away from FIFA's control
"The president of FIFA has to be a fair, a serious and a very democratic gentleman," he told Sky Sports News.
"Mr Blatter is now re-elected for the next four years and I'm very curious: is he fit for all these requests? I am not convinced that is true.
"There is no sign. He has been running in this position since 1998 - so 13 years in a row - and I would say it's normal that you're not convinced by his last period as president, that he is fit for all these requests."
Blatter was the only candidate to stand for the presidency in June after Mohammed Bin Hamman withdrew amid claims of corruption and vice-president Jack Warner resigned from his post.
Rummenigge was not surprised by the decision, insisting that the world's national football federations stood by him because they are FIFA's priority and get "everthing done in their favour."
But he is determined to make sure the ECA and its members are given a greater say in how the game is governed.
"First of all my request is not just focussed alone on clubs and it is not just to get more power," he said.
"My request is not getting more power, it's about having more democracy and more governance and I believe it's a quite normal request. I would like to request that not just clubs, but leagues, referees and women players have to be included in the decision-making.
"If Mr Blatter and his colleagues are ready to do that, then fine. If not, we will have to see what we can do to convince him."
Rumennigge though, does not believe that would involve a new league that would see Europe's top clubs leave their national federations to form an independent competition.
The ECA has taken over from the G14 group, who first raised the issue of a breakaway league, featuring the leading club sides from Europe's top leagues, including Manchester United, Chelsea, Liverpool and Arsenal from the Premier League, Barcelona and Real Madrid from La Liga, the two Milan clubs and Bayern Munich.
Rummenigge acknowledges that the threat was there, but insists it would now be too big a shake-up - and one that he is not prepared to push through.
"In the past when we had the G14 there was a clear plan on the table to have our own league guided by ourselves," he said.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.