The Okhla MLA, who held the post for nearly 6 months, had in September last year resigned amid allegations of irregularities.
The process for constituting a new board having seven members is on. Khan was elected as a member of the body last week.
Sources said Khan's election as chairman was "almost certain" and would materialise after nomination of four members of the Board by the Delhi government.
"A file on nominated members, including a government officer, Islamic scholar, social activist and one Bar Council member, is lying with the Lt Governor. After his nod, the Board will elect its chairman," the source said.
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Two other elected members of the Board are Congress Rajya Sabha MP Parvez Hashmi and Chaudhary Sharif. The latter has been elected from the Mutwalli (manager) quota.
Khan's previous stint as Waqf Board chairman was marred by allegations of corruption and investigation and raids by the Anti-Corruption Branch (ACB).
He was elected chairman in March 2016 and had resigned 6 months later after an ACB raid on the Waqf Board office in connection with an alleged recruitment scam.
Thereafter, a case was registered by the CBI to probe alleged irregularities during Khan's chairmanship of the Board in November 2016.
"Although he was suspended over the issue, Khan has now not only regained his previous posts and status, he is just about to be the chairman of the Board," he said.
BJP's Leader of Opposition in Delhi Assembly Vijender Gupta said he will raise the matter with Lt Governor Anil Baijal.
"The Kejriwal government is set to make Amantullah Khan the next Waqf Board chairman even as the CBI is probing a case of criminal breach of trust against him," Gupta said.
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