He recalls: "I was meant to have a meeting with Benjamin Netanyahu, but then, at the last minute, I met Mr Gendleman. I told him about the need for more diplomacy. Israel only spends eight per cent of its Foreign Ministry budget towards diplomacy. They could do more. I also said, they should never receive anyone secretly. They asked me if I wanted my visit to be a secret. I said, no, of course not."
He believes anti-Israel "propaganda" in the Muslim world needs to be combated. He dismisses the boycott movement as doing more to harm than good to Palestinian rights, and he says Israel needs to put more effort into building ties with Arab leaders.
But Mr Al-Sharifi, who lives in London, was not always so supportive of the Jewish state.
He says that, like so many, he was fed a negative image of Israel.
"You think all Israelis are murderers. I had this image for years. It comes from the schools, media and mosques. You can call it brainwashing. They are poisoning our minds.
"There was one story about Israel that always stuck in my mind. Fifteen years ago, I was in London watching an [Arabic news channel]. It said that Israel was importing a 'Norwegian rat' - a big rat that they fed and released into the Arab territories. And what does the rat do? It eats the feet of newborn babies.
"It was such disturbing news. I would look at my children's feet and think of it. Imagine that propaganda."
So it is unsurprising that the father-of-two "never thought I would go to Israel". But, in October, he was called by an Israeli journalist about a re-interpretation of the Koran that Mr Al-Sharifi had created for his organisation, Liberal Muslims.
The publicity from the article attracted interest from the Ministry of Foreign Affairs, which invited him to Israel two months ago for a five-day visit.
He flew El Al and stayed in Jerusalem's Crowne Plaza hotel. He woke up at 6.30am every morning for back-to-back meetings until midnight. He visited projects preparing Arab students to enter the hi-tech industry. The trip changed his perception of Israeli Arabs.
"I had a bad image of them before," he says. "But they are Israelis like everyone else. They are Arab in origin and Muslim in faith, and no one has a problem with them. I went and saw so many pharmacies in Tel Aviv. Most people working in there were in hijab. I saw big Arab villages. There is freedom."
During his stay in Israel, Mr Al-Sharifi visited Temple Mount, making him one of the few Muslims living outside Israel and the Palestinian territories allowed to visit the site. Was he emotional?
He starts to play with the prayer beads in his left hand.
"You want the truth," he asks. "No. I was not welcomed at the Al Aqsa mosque because they called me a friend of Israel, because I had not travelled through Jordan."
Still, he plans to return to Israel and meet representatives from the PA, and is even open to the idea of being Iraq's ambassador to Israel.
"When I came back from Israel, as a man in the middle of Muslim-Arab society, I tried to tell them what Israel is really about," he adds.
"I need to take people to Israel. I spoke to one tribal leader from southern Iraq when I got back. He said he would come. That man alone, two million people do whatever he says. We need people like him to go to Israel and tell their [communities] what they see.
"They can go to Israel and see the advancement in technology, medicine and security - things we need. And Israel is willing to share this. What does Israel want in return? Our blood? No, they want peace and recognition."
For Mr Al-Sharifi, battling anti-Israel propaganda is key. "A 'Zionist' is a swear word. We are now living in the 21st century. We cannot pass the messages we heard from our ancestors on to the next generation. How do we stop it? We stop it by telling them the truth."
It is an unconventional stance to take, but not so surprising if you look at Mr Al-Sharifi's background.
Born in Baghdad in 1959, he was forced to flee to the UK in 1980 as a result of anti-Shiite sentiment under Saddam Hussein, a Sunni. After summer school stints in Oxford in the 1970s, he studied at a college in Burnage, Manchester.
Aged 21, he went on to read economics at Karachi University in Pakistan. There, with friends, he set up a group opposing Saddam Hussein's regime.
His father - who learnt his trade, importing and exporting crockery at Baghdad's Shorja Market, from a local Jewish businessman - was forced to officially disown him.
He received training from American officials in Washington with a view to establishing a post-Hussein government. He went on to help form Iraq's Defence Ministry after the toppling of Saddam in 2003. He survived assassination attempts, one of which left his right arm with limited movement.
He served as Iraq's envoy to Kuwait from 2005 to 2006, before working at the Iraqi embassy in Jordan.
With time on his hands, Mr Al-Sharifi took a strong interest in the rise of Islamic fundamentalism and the concerns that terror groups were taking words in the Koran verbatim.
Inspired by Reform Judaism, he launched Liberal Muslims in the UK. The fact that he is not an authorised religious scholar or an imam does not concern him. "Why can't I do the same, why can't I be an imam? Now I am not a Shiite or Sunni. I am liberal."
