Elstone revealed 'genuine conversations' are taking place regarding ownership and future investment but there was a responsibility to select the 'right buyer with the right intentions'.
Indian construction giant Jain were the latest to be linked with a move and although it is understood that while officials met for informal talks there was no movement on the issue.
For sale: Everton are open to talks with potential new investors
Toffees' chairman Bill Kenwright has come in for criticism over the past couple of months from a section of fans who believe he is the main barrier to progress on the sale.
Supporters' group The Blue Union are staging another rally and march before Everton's home match with Wolves a week on Saturday as they continue to protest about perceived inertia at boardroom level.
? However, Elstone said the process was a complicated one which had to be handled sensitively.
'Speculation and football go hand in hand and over the past few weeks there's been plenty of talk about Everton takeovers and investment,' he said.
'As we've said repeatedly there's been a constant stream of interest and dialogue over a considerable period of time and right at this moment that remains true.
'There are a number of individuals, groups and companies interested in Everton and genuine conversations are taking place about future ownership and future investment.
'Discussions are still at an early stage. What I know to be absolutely the case is the first question asked by us in these discussions is never "How much?" but always "What are your thoughts, intentions or plans for Everton's future?"
Open to offers: Everton chairman Bill Kenwright wants to find the right buyer with the right intentions
'The responsibility to find the right buyer is paramount and not an excuse for "not really for sale", "wanting too much for it" or 'wanting to stay involved'.
'Such a negative outlook only hinders a painstaking and challenging process made all the more difficult in a recession-hit world.
'I'm tired of saying it but the club is absolutely for sale and has not, and will not fail to be sold because it's too expensive or comes with onerous conditions.
'We sincerely hope the right buyer, with the right motives, with a commitment to take Everton forward is part of this current dialogue.'
Elstone also moved to defend the club's financial position after yet another transfer window went by when the Toffees' income exceeded their expenditure.
Midfielder Mikel Arteta and strikers Jermaine Beckford and Ayegbeni Yakubu were sold to Arsenal, Leicester and Blackburn respectively for about ?15million.
Loan signing: Royston Drenthe was one of the few signings manager David Moyes was able to make during the summer transfer window
Only loan signings Royston Drenthe and Denis Stracqualursi and free agent James McFadden have arrived as replacements.
But with the club's debt running between ?40m and ?45m Elstone admits there is a fine balancing act to be done.
'Speculation is also once again fuelling debate in certain quarters about where our money goes,' he told the club's official website.
'To get this straight again, almost 85p in every ?1 we earn is spent at the training ground and academy paying the players, the coaches, the scouts, the conditioners, the medics, the support teams, team travel and accommodation along with rent and other overheads.
'We're confident that the investment pays off. What's left in the coffers, the other 15p in the ?1, funds everything else.
'Quite simply, it doesn't allow us to waste a penny. It means we're a 'lean ship' and one of the leanest in the Premier League.
'It means in some areas, resources are stretched, more stretched than I'd like them to be if I'm honest.
'It certainly means we all have to pull our weight.'
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Source: Daily Mail
Source: Daily Mail