Speaking to the US television programme 60 Minutes, Sheikh Tamim Bin Hamad Al Thani said Trump plans to bring the Persian Gulf neighbors together in a bid to mediate in the dispute, Al Jazeera reported.
Saudi Arabia, the UAE, Egypt and Bahrain cut ties with Qatar on June 5 and imposed a land, sea and air embargo, accusing it of supporting "terrorism".
Doha vehemently denies the allegation and has repeatedly called for an "unconditional dialogue based on mutual respect for sovereignty".
"It is true he [Trump] suggested that we come," Sheikh Tamim told CBS News' 60 Minutes. "I told him straight away, 'Mr. President we are very ready, I've been asking for dialogue from day one'."
When asked by host Charlie Rose about the blockading countries' reaction, the emir replied: "It was supposed to be very soon, this meeting, but I don't have any responses."
Trump has previously said he supported the mediation efforts of Kuwait, but if that did not manage to resolve the Persian Gulf crisis, he would be "willing to be a mediator".
Sheikh Tamim's full interview with 60 Minutes will be broadcast on Sunday at 23:00 GMT.
It took place in the Qatari capital of Doha in early October, a few weeks after the emir and the US president met on the sidelines of the 72nd United Nations General Assembly in New York.
Speaking to reporters after their meeting on September 19, Trump called Sheikh Tamim a "long-time friend" and said he had "a very strong feeling" that the Persian Gulf crisis "will be solved pretty quickly".
For his part, Sheikh Tamim said Doha and Washington had "a very strong relationship" - Qatar is home to the largest US military base in the Middle East. He also said that he believed Trump's "interference will help a lot" in the dispute.
In his interview with Rose, the Qatari emir also said he is worried about chaos in the Middle East if the Persian Gulf diplomatic crisis continues to escalate.
"I'm fearful that if anything happens, any military act happens, this region will be in chaos," said Sheikh Tamim.