Hotels were booked out when the city was announced as the host for the event but, as it gets closer, rooms are becoming available.
One hospitality industry group suggested people may have been forced to cancel rooms due to train strikes.
They will cause disruption for those travelling by rail to the contest on the Friday 12 and Saturday 13 May.
The RMT Union leader Mick Lynch denied Eurovision was deliberately targeted.
"We don't pick out events in our union," he said last weekend.
"We don't say 'we'll disrupt that event, or we'll disrupt that event', we want to go on strike on Saturdays because it's the busiest day on the railway."
Kate Nicholls, the chief executive of UK Hospitality which represents more than 740 companies, told BBC News: "It's a great shame that a rail strike is being held during the event, which can force people to change or cancel plans.
"I would encourage fans to continue looking for availability if they're planning to stay in Liverpool. It's great to see that so many fans will be in Liverpool for the big event and will be staying in the city."
BBC News has seen availability on hotel booking sites for around £200 a night in many hotels - from Tuesday 8 to Sunday 14 May.
Next week there will be two-semi finals of the competition on Tuesday and Thursday, ahead of the grand final on Saturday.
It's the first time in 25 years the world's largest music event is being held in the UK, which is hosting it on behalf of last year's winners Ukraine.
The contest is expected to draw around 100,000 extra visitors to the city over the next 10 days.
In March Booking.com confirmed to BBC News "some accommodation partners had been targeted by phishing emails" which was putting customer's data at risk.
A number of fans of the song contest contacted the BBC's Eurovisioncast podcast outlining their experiences of almost falling for scams relating to accommodation booked for Eurovision.
Booking.com said it had "actively been supporting our partners, as well as any potentially impacted customers" and continued "to make security and data protection a top priority".
Customers are advised to speak directly to their hotels if they have concerns.
About 6,000 fans will be inside the arena for each of the nine ticketed shows - the three televised ones and six production previews that double up as rehearsals.
Outside of the venue there are a number of free events taking place across Liverpool as part of its two-week cultural festival.
They include a simultaneous rave between the city and Kyiv, and a fan zone where 15,000 people can watch the contest on big screens.