The Cherries have been in administration since February
Two new bids to buy Bournemouth were lodged with the League One club's administrators on Friday, with a third set to follow in the next 24 hours.
The news follows the collapse of a proposed takeover by preferred bidders EU UK Ltd earlier this week.
Administrator Gerald Krasner told BBC Radio Solent: "I have two bids in writing and could get another.
"Whoever lodges their deposit monies with me first will get exclusivity on the deal."
He added: "I'm not going into who the bids are from, or the financial details involved, but when the deal moves forward and the monies are in the bank, then we'll go public."
After the EU UK Ltd deal fell through, Krasner had warned that he may have to sell players if no new deal had materialised by the end of the week.
The Cherries, who are battling to stave off relegation to League Two as well as battling to stay afloat off the pitch, travel to Walsall on Saturday - where they will be relegated if they lose and Crewe avoid defeat against Cheltenham.
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