Leeds is one of seven cities in the UK shortlisted to host the singing competition next year, with the successful city due to be announced in the next few weeks.
The competition would fall in the middle of Leeds' Year of Culture, which aims to encourage people in the city to get creative.
Broadcaster Logan, chair of Leeds 2023, said: "I know that maybe in the bookies eyes Leeds isn't the favourite at the moment, but I think creeping up on the outside and being the dark horse isn't a bad thing.
"Leeds has everything that they want. Fingers crossed the good news might come in a few weeks or so."
Logan previously hosted Sports Personality of the Year at the Leeds Arena and said the Eurovision hosts the BBC were "blown away at that venue" and it would be "brilliant" for the song contest.
Gabby Logan talks to ITV News about Leeds 2023.
Eurovision 2023 is being hosted in the UK on behalf of Ukraine, who would normally have the rights to stage the event having won this year's contest.
Logan told ITV News: "Leeds has got a huge link with the Ukrainian community - the biggest conurbation of Ukrainians outside of London is in West Yorkshire.
"That's really important as well to the feel of the whole event - that Ukraine is very much a part of it."
Leeds 2023, dubbed the year that will "let culture loose", will kick off with an opening show of music, dance and poetry at Headingley Stadium.
The organisers explained at an event on Friday, 23 September that the only way to get yourself a ticket is to send your own piece of art to be entered into a ballot.
Logan added: "We want people to get busy being creative because we think that kind of personifies the spirit of Leeds 2023. It's by the people of Leeds for the people of Leeds."
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