The PCB will meet on Tuesday to discuss Inzamam's successor following their shock first-round elimination from the World Cup and subsequent death of coach Bob Woolmer which is being treated as murder by Jamaican police.
Inzamam, who was appointed in 2003 and quit on March 18, has pushed for senior batsman Younis to take over his old job.
"Younis is not comfortable leading the team at this stage as he believes he doesn't have the required widespread support within the team," the board source told.
"He is also reluctant as he doesn't see wide support in the cricket community for him to replace Inzamam."
Younis lost some face last year when he refused to lead the team in the ICC Champions Trophy in India in place of the banned Inzamam.
He was dubbed immature and volatile after he changed his mind at the eleventh hour following reported differences with then chairman, Shaharyar Khan, and some players.
Shaharyar was, however, replaced by Nasim Ashraf, a smooth-talking bureaucrat two days before the team's departure and he managed to convince Younis to captain the side.
Younis had a miserable time in the Champions Trophy winning just one game and faced the wrath of the media and public.
Rashid Latif, a former Pakistan captain, felt that Younis should refuse the captaincy. "I don't think this is the right time for him to come in. Some people obviously doubt if he is mature and strong enough to lead the team after the World Cup," quipped Latif.
"It would be better for him to concentrate on his batting and come in as captain when he feels comfortable and there is full support for him."
Former World Cup-winning captain Imran Khan backed Younis to take the job. "He must not refuse. If he didn't want to captain he should not have accepted to become vice-captain."
If Younis does refuse the captaincy, senior batsman Mohammad Yousuf, who has captained before would be the logical choice to step in but sources said that young all-rounder Shoaib Malik is also under consideration.
Former Test paceman Aaqib Javed was tipped by media observers as likely to be named as coach, succeeding Woolmer.
Pakistan were trying to arrange a one-day series with Sri Lanka next month in Abu Dhabi.