Speaking to Premier, Rt Rev Mike Hill said: "On the face of it all it all seems rather odd. I don't know whether there will be some under the radar discussions and some assurances about their financial support while they're here."
The men had been refused entry into the country because the Home Office thought they were 'too poor'.
The Syriac Orthodox leaders - Archbishop of Mosul Nicodemus Daoud Sharaf, Archbishop of St Matthew's Diocese Timothius Mousa Shamani and Archbishop Selwanos Boutros Alnemeh of Homs - had been invited to Britain in order to attend the opening of the UK's first Syriac Orthodox Cathedral last month.
One clergyman was told it was against UK Government policy to grant a Syrian a visa.
Bishop Mike, who is sitting in the House of Lords this week, added: "The government was anxious they might try to claim asylum whilst they're here. The Government's - and successive governments' - approach to asylum seekers has been a bit of a mixed bag.
"I'm hoping there might be some further discussions that will pave the way for these men to come and I hope they make it."
In a statement issued by the Home Office over the weekend, a spokesperson said: "All visa applications are considered on their individual merits and applicants must provide evidence to show they meet the requirements of the immigration rules."