"Hopefully, applications will be many and competition will be fair", he told reporters.
Asked to comment on the growth of LUKOIL share prices and today's quotations exceeding the initial price, Gref said: "The initial price should not depend on market fluctuations".
This initial price was calculated from the trend over several years and the last half year.
"The final (selling) price (of the LUKOIL state block of shares) will be set depending on the market price as of the day of auction", Gref said.
The initial price is 1.928 billion dollars.
Gref would not say what he knows about the applications filed.
The Russian Federal Property Fund continues receiving applications for the auction, due to be held on September 29.
So far, only ConocoPhillips and David Guggenheim, representing the Dabir International company, have voiced the desire to participate. Russian companies have not yet followed suit.
The Property Fund hopes that the end price will the same as LUKOIL's market price as of the auction time or even higher. The initial price has been set at 29.83 dollars per share.
The RIA Novosti-polled experts unanimously say it is a fair price.