The rent on the 08 Place is £220,000 a year, and its hi-tech TV screens cost £60,000 to run annually.

Cllr Millar said: “My view is that, in February, 2014, when the lease ends, we need to have an exit strategy.

“Whitechapel was right when it was created. We didn’t have Liverpool One, we didn’t have the Metquarter.

“Now I think there is a need to have a tourist point, but I don’t see it as being the same as the 08 Place.

“I don’t see the 08 Place continuing beyond February, 2014.

“If we can sublet the building before 2014, it should not stop us making our plans earlier.”

The Whitechapel venue operates as the city’s main tourist information centre, and opened in August, 2005.

The ground floor of the complex is occupied by council staff and provides information, event tickets and souvenirs to visitors ,while the top-floor office space is leased out by Chas Cole’s firm, CMP, which runs the Summer Pops.

It has been controversial from the start after the £1.4m Neighbourhood Renewal Fund – cash intended to help regenerate the city’s poorest areas – was used to help pay for the £2.2m fit-out and furnishing of the building.

When concerns were raised in February, 2005, then council leader Mike Storey insisted: “This will not be a cost on the council tax payer.”

Months later, a council report revealed the 08 Place would notch up a deficit of £161,000 a year, a total of more than £800,000 between then and 2010.