In September 2005 Ayman Nour of Al Ghad Party and No'man Goma'a of New Wafd Party nominated themselves against President Hosni Mubarak . Nour was charged with fraud and Goma'a was accused of insanity!
Since 2000, Gamal Hosni Mubarak  has the been groomed to be his father's successor as the next president with no apparent opponent. In August 2009, Gamal Mubarak launched his Sharek [participate] initiative  where he launched an open online forum (Sharek) where he promises to address all the questions posed by young internet savvy Egyptians himself. Later on, Egyptian singer Mohsen El Sayad decided to campaign for Gamal Mubarak in his own way [Arabic Song]. The song is titled Gamal Mubarak … Why Not? 
Rumor has it that Omar Soliman , Chief of the Egyptian General Intelligence Services , is an eligible presidential candidate. In June 2009, a blog  and Facebook group  were dedicated to support Omar Soliman.
Today Mohamed Abdel Salam of Bikya Masr reported: Coptic lawyer throws hat in for Presidential run :
In a new unprecedented move, Coptic lawyer Mamdouh Ramzy declared his willingness to nominate himself for Egypt’s 2011 presidential elections, becoming the first person to put his name forward for a possible run for the country’s top job. Razmy said in an exclusive interview with local newspaper al-Youm al-Saba’a that the rumors concerning his candidacy were true.
“I am the first Coptic Egyptian that will run for the presidential elections, after meeting all the requirements prescribed for nomination to this post, which is the first top post in Egypt,” he said.
As for the Church's stance, the blogger notes:
The Orthodox and Protestant churches in the country welcomed the decision by the prominent Coptic lawyer to run, saying that this decision is evidence of national unity, due to the existing conditions for a presidential candidate. Ramzy is a leading member of the Constitutional Party.
However, the country’s Catholic Church said they consider the nomination as “contrary to the constitution.”
Priest Salib Matta Sawiris, a priest at the Church of Saint George, said that “the church welcomes the first Coptic to participate in the political life with this idea that he wants to nominate himself for the post of President of the Republic.”
But, he argued that it is not easy and that “it makes sense that a candidate for this position would be a candidate following the religion of the majority,” meaning a Muslim. Sawiris explained that the church welcomes any Egyptian meeting the conditions for the nomination, but he sees this as “a waste of time,” because when someone wants to lead an electoral campaign, “there must be a study and a plan before doing so.”