Both clubs are considering moves away from Anfield and Goodison Park and previously there have been talks of the option of groundsharing.
“There’s the possibility of building a new stadium at Stanley Park; the one thing I will say is that there have been rumours that we’re interested in the possibility of a share with Everton,” Werner told Sky Sports News.
“I won’t ever say it completely [ruled out], but our fans don’t want it so I think it’s a non-starter.”