But if costs rise then he is prepared to abandon the project.
"It would be crazy to say there is no risk," said Parry. "There is a risk, but we believe it is justifiable.
"We feel we can afford the construction costs of £80m. If it rises much above that we will pull the plug."
The club are due to have further talks with Everton, the City Council and Liverpool Vision and the North West Development Agency regarding a possible shared stadium, but Parry insisted that it is not what the club want.
"There has been a strong reaction from our supporters over the shared stadium issue," he added.
"The vast majority are against it and this is a weight of opinion that cannot be ignored."
