"It will be a bit of hand fighting between Channel nine and ABC for the third," he said.
The National Press Club also expressed concern that its proposals for national debate, given to all television networks at the highest level, were not taken over by major parties.
The headquarters of the coalition campaign sparked the dispute by issuing a statement Friday morning, saying it wanted more debates, but Mr Shorten refused because he expected voters to "dirty" him.
Mr Morrison intensified the attack, saying he was happy to debate Mr Shorten, in addition to the two debates next week.
"I'm happy to debate with Bill Shorten. We have two that follow this week, but for some reason he does not want to have them in the last two weeks of the campaign," he said.
"I'm happy to have nine with nine, on Monday we have seven with seven. We have one with Sky at the end of [next] week. I would be happy to have one with ABC.
"I personally have been in contact with [ABC television host] Lee Sales. I said I would be very happy for Lee Sales, Bill Shorten and myself in the same room. Good to me.
"The question is: why does not he want to do it?"
Mr Morrison said Mr Shorten had a "presumption" that he would win the election.
"Bill needs to get out of the coronation tour and he should be involved in the campaign," he said.
Several weeks were needed to agree Coalition and Labor campaign teams to agree on both debates, worrying that there will be no time for a major national debate to be broadcast for all Australians in the last weeks of the campaign.
The debate on Monday is hosted by Western Australia the newspaper and the seven networks and will be broadcast on a channel with a lower rating 7TWO instead of the main channel on the network. It will be broadcast at 19:00 AEST.
The debate in Brisbane on Friday, May 3, is a "People's Forum" hosted by Sky News, which is broadcast at 6:30 pm.
Nine Entertainment, owner of Sydney Morning Herald and Time, sent a proposal for a debate on the two major parties in early March. The coalition wants to accept the offer, but labor has so far refused.
The chief executive of the National Press Club, Maurice Riley, said: "The National Press Club made a submission to hold a debate for the leaders. The club was a traditional place for debate among the leaders in the previous elections, and we made it the first one in 1984.
"In the absence of a debate committee, which is well established in other countries like the United States, the National Press Club is the most trusted neutral place to hold debate, as it will provide it to every network at the highest level.
"We are disappointed that we are not doing it."
The political editor of nine networks, Chris Uhman, said: "Nine news offered to host the debate of leaders at the highest level in our main channel in the last weeks of the campaign. The Liberal Party agreed in principle, said Labun."
ABC News Director Gauen Morris also said that Shorten refused an invitation to debate.
"The ABC also called on the prime minister and the leader of the opposition to discuss radio and television and ABC information platforms to the national broadcaster. The opposition leader rejected the invitation," said Maurice.
David Crowe is the chief political correspondent of Sydney Morning Herald and The Age.