Spanish authorities agreed to allow Dr Haytham Manna and Dr Lugaa Abu Yahia to visit Alluni, who is detained in Spain. Although government doctors were available to Alluni, this is the first time for physicians of his choice to be allowed access.
The decision comes amid mounting international pressure on the Spanish authorities to release Alluni.
Manna, spokesman for the Paris-based Arab Commission for Human Rights, said he was planning to visit Alluni towards the end of next week.
"At Taysir's request I shall be visiting him for the first time since he was arrested."
Alluni's wife, Fatima al-Zahra, said she worried about his health. Alluni has a serious heart condition.
Al-Zahra told Aljazeera.net: "We applied to the authorities to allow the doctors to visit Taysir three months ago and only heard the decision now. He is still very ill.
"We have not heard any new information on his trial, and I feel quite pessimistic about his release."
Spain's Interior Ministry was unable to comment immediately.
Talks with Zapatero
"In the Arab world we are used to being detained first then questioned later, but we do not expect this in Europe"
Dr Haytham Manna
After Manna and his colleagues visit Alluni, they plan to hold talks with Prime Minister Jose Luis Rodriguez Zapatero.
"We are preparing a delegation of six Arab intellectuals to meet with Zapatero. He is a man of peace, a real democrat," said Manna.
"I think there is international pressure on Spain to show it is taking measures against terrorism. That is why Alluni was arrested. He is just an innocent victim in all this.
"In the Arab world we are used to being detained first then questioned later, but we do not expect this in Europe," he said.
Syrian-born Alluni, a father of five, was arrested in September 2003 at his home in Granada.
Al-Zahra told Aljazeera that her husband was arrested on suspicion he misused his position as a journalist to carry out an interview with Usama bin Ladin, during which the latter called for jihad.
Alluni was released on bail on medical grounds about a month later. He has a serious heart condition.
However, he was re-arrested in November 2003 for fear he may flee the country while awaiting trial.
Alluni's continued imprisonment has sparked outrage among Arab human rights groups, journalists and colleagues, who describe his prosecution as an attack on freedom of the press.