Christian Purslow told BBC Radio he would not put a time limit on how long it would take to made a decision, saying he now needed to sort through the bids.
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"We have just received some written bids at this stage, and it would be wrong to characterise anybody as a front-runner," he said. "We have had a number of bids (and) will take time to examine those extremely carefully."
Purslow was speaking following a report in the Sunday Times which said Royal Bank of Scotland, a major creditor of Liverpool, could take control of the club after a search for a buyer proved fruitless.
The newspaper quoted sources close to the talks as saying that none of the potential buyers could prove they had the money.
RBS said in a statement that it continued to have confidence in the sale process and said it was not making preparations to take control of Liverpool.
Purslow declined to comment on the report beyond saying that it sounded rather speculative.
"We have excellent relations with our lead bankers RBS, we've been in constant dialogue with them... and I am extremely comfortable with that working relationship," he said.
According to British media reports, as many as six potential parties had looked at buying the 18-times English league champions. The club is expected to fetch a price tag of around 400 million pounds or more, bankers have told Reuters.
Liverpool's unpopular American owners Tom Hicks and George Gillett put the club up for sale in April.
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