Pakistan's Foreign Minister Khawaja Asif, who recently visited the US, told the VOA Urdu in Washington that his country would play a leading role in this quadrilateral session, aimed at bringing the Afghan Taliban to the negotiation table.
So far, five sessions of the QCG have been held, with the last being held in May 2016 in Murree, Pakistan.
The peace efforts has been plagued by problems from the beginning. First, the Taliban refused to join it demanding the same status as that of the Afghanistan government. When they were persuaded to attend the meet, relations between Kabul and Islamabad became strained.
The international community also welcomed the quadrilateral talks as the four countries are seen as crucial for ensuring the success of any peace talks on Afghanistan.
China's participation in the talks was particularly encouraging as both Pakistan and Afghanistan set aside their acrimony to welcome China.
Pakistan hoped that China's involvement would answer its main concern, India's growing influence in Afghanistan.
The Afghanistan government hoped that China's clout with Pakistan could have help persuade Islamabad to improve its ties with Kabul.
But, during the fifth session, some officials in Kabul leaked news to the media saying that the reclusive Taliban leader Mullah Omar had died in Karachi in 2013 but Pakistan was hiding this news because it feared losing its influence on the terror group.
The revelation derailed the talks as officials from each of the four governments opted to return to their capitals for consultations.
In May 2016, Mullah Omar's successor, Mullah Mansour was also killed in a US drone strike in Balochistan, which further delayed the peace process.
Since then, Pakistan has made several attempts to restart the talks but none of the four parties seemed very keen on returning to negotiation table, the report said.
In Afghanistan, the Taliban increased their attacks on both the US and Afghan government targets. And in the United States, the new Trump administration concluded that the best way is to force the Taliban to talk.
At a recent news briefing in Washington, US State Department spokesperson Heather Nauert expressed doubts about the success of these peace efforts when she questioned the efficacy of the Taliban's non-official diplomatic post in Qatar.
"We have been now in that war for 16 years" but "they have not been able to come to any kind of peace and reconciliation, so just by having folks sit around in Qatar, in probably a pretty cushy life there, has not demonstrated, has not brought to the table any kind of significant peace efforts," she said.
And during his three-day visit to Washington last week, the Pakistani foreign minister acknowledged that Pakistan too was losing its influence on the Taliban.
"At least for our influence on Taliban today, there is mistrust," Asif said, adding that he believes Russia "today has more influence on the Taliban than Pakistan does".
Despite these concerns, all four members of this group want some peace in Afghanistan and are likely to participate in the Muscat meeting, the report said.
But instead of sending their senior officials, as they did in the last five meetings, they are likely to send mid- level officials to prepare for future talks, it added.