The Dons' planned move to Milton Keynes suffered a blow on Friday when officials from The National Hockey Stadium ruled out a temporary switch of the Division One side to their complex for next season.
Despite Wimbledon's intentions to move into a new stadium in Milton Keynes in the future, the club announced that it would be their intention to start next season playing their home matches back at Selhurst Park.
However, Alexander has claimed The Eagles have had no contact with The Dons and, as it stands, they do not plan to have Wimbledon playing their home matches at Selhurst Park next term.
"We have had no contact whatsoever with representatives from either Wimbledon Football Club or their administrators," Alexander told the club's official website.
"As far as Crystal Palace Football Club is concerned, Wimbledon FC will not be playing at Selhurst Park.
"Until such time as we might have communication with Wimbledon FC or their administrators, this situation will remain."
Meanwhile, Palace manager Steve Kember has revealed his hope of keeping Hayden Mullins at the club but admitted that Julian Gray will likely move on, after turning down a new contract offer.
"Hayden's agents say he doesn't want to sign a fresh contract with us but he hasn't said that to me personally and I will be speaking to him about it," said Kember.
"From the club's point of view, if we're to get any money for Hayden we need to do it now."
"We can't wait until the end of next season, otherwise he'll walk away for nothing.
"Julian has turned down the contract we offered so we will have to wait and see who comes in for him."
