The Daily Mail says Cellino has been heavily linked with a takeover bid at the crisis-stricken south London club and reports in Italy have suggested he is 'very close to an agreement' to buy Palace.
But the 53-year-old Italian, who is president of Serie A club Cagliari, would face a huge fight to pass the Football League's fit and proper person test, having two previous suspended jail sentences for deception.
Guilfoyle said: "I want to talk to anyone who has the right intentions for this club. But after hearing about his convictions and the problems that would bring up with the fit and proper test then there doesn't seem much point."
He added: "We've had five interested parties in the club and we are pressing ahead to a conclusion as soon as we can. I'd rather not be here into the close season."