Anderson was speaking after it was confirmed the club will not now be pushing ahead with a project to build a new stadium on Walton Hall Park.
It is the third time Everton have seen plans for a new stadium collapse after failed attempts to relocate to Kings Dock in 2003 and Kirkby in 2009.
The club have confirmed that they have already identified two brownfield sites within the city boundary and are working with the local council.
Speaking to BBC Radio Merseyside, Anderson said:
"I’m confident the new stadium will be up and running in three years time.
"I think there is a real acceptance by them and I’m pretty confident that within three years there will be a new stadium for Everton football club in Liverpool."
Given Everton have now failed to move three times in 13 years it seems ambitious to suggest they will be in a new ground within three, especially as they haven't finalised a site yet.
Unless, of course, Anderson knows more than he is letting on.
The WHP project has been a lame duck for a while now so it may well be that new majority shareholder Farhad Moshiri has been on the look out for alternative sites since February.
If the club can find a site over the summer and Moshiri can ensure funding, building work could in theory begin as early as next summer with the aim of being in for 2019.
That remains highly ambitious though and after years of false promises I'm not getting my hopes up.