If the proposal is not successful, Allam is considering an alternative site in Melton, East Yorkshire.
He told BBC Radio Humberside: "It was a friendly meeting. It went well. I'm more hopeful [of getting the plans through] than before the meeting."
The Egyptian multi-millionaire bought the club last year.
He went on to plough over ?30 million into the Championship side, but for either project to progress much more will be needed.
Allam added: "My architectural consultants have quoted me detailed estimates, totalling ?114m if the project is at the KC Stadium or ?161m if the project is built at the Melton site.
"I'm expecting something like 20% of my money to go there as a deposit. We'll then be able to borrow against the mortgage on the site and hopefully we can get sponsorship from Sport England, the council, many other sources, so it's a combination."
Just last week
Allam donated ?1m to Hull Kingston Rovers
because he realised he had "done nothing for East Hull" since moving to the area in 1968.
Source: BBC Sport
Source: BBC Sport