The Sudanese leader is the subject of two International Criminal Court arrest warrants, issued in 2009 and 2010 over his alleged role in Sudan's brutal counterinsurgency campaign in Darfur.
He faces charges of genocide, crimes against humanity and war crimes.
"Jordan would be defying its international obligations as an ICC member if it allows al-Bashir to visit without arresting him," said Elise Keppler, associate international justice director at Human Rights Watch.
"Welcoming an ICC fugitive would undermine the Jordanian government's recent efforts to strengthen the country's rule of law."
Jordanian authorities have not commented on whether they will be allowing al-Bashir's first visit to the country as an ICC fugitive.
Since the issuing of the ICC arrest warrants, members of the international court, including Botswana and Denmark, have affirmatively signalled that the Sudanese president faces arrest if he enters their territory.
Other nations have relocated meetings or called for Sudan to send representatives on their behalf.
In 2012, Malawi opted to relocate the an African Union summit after AU members insisted that al-Bashir be allowed to attend. In 2010, an international conference in Kenya was relocated to Ethiopia over similar concerns.
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