Mr Paphitis was among a number of parties interested in Woolies.
Dragons' Den entrepreneur Theo Paphitis has pulled out of the race to buy parts of troubled retailer Woolworths.
Mr Paphitis, who has been named among potential bidders for the collapsed retail chain, said it was not possible to reach a deal with administrators.
Mr Paphitis was believed to be working on a plan to rescue some of the chain's most profitable stores.
The administrators from Deloitte said earlier this week that there had been "substantial interest" in the firm.
Theo Paphitis was also thought to be willing to preserve the Woolworths brand.
"Unfortunately, the constituent parts of Woolworths are more valuable than the whole. The administrators have a difficult job to do and I appreciate that they need to get the highest cash value for the business," Mr Paphitis said in a statement.
"I hope that an alternative proposal succeeds in securing the future for the many Woolworths employees involved," he added.
'Against the clock'
WHAT IS ADMINISTRATION?
A rescue mechanism for UK companies in severe trouble. It allows them to continue as a going concern, under supervision, to try to trade out of difficulty
Ardeshir Naghshineh, Woolworths' largest shareholder, has been also reported to be preparing a bid.
It is thought that Sainsbury's, Asda, Tesco, the Co-op and discount chain Poundland also want to pick up some of Woolworths' prime stores.
However, the BBC understands that no deal is likely to be announced immediately and it is unlikely that any one buyer would take control of the entire business.
Mr Paphitis has revived the fortunes of several companies, including stationers Rymans and the La Senza lingerie chain.
Woolworths' retail and wholesale operations went into administration last week, putting the jobs of 30,000 staff at risk.
In addition to 815 stores and four distribution centres, Woolworths owns Entertainment UK, which distributes DVDs to supermarket groups and other retailers.
The company and BBC Worldwide are joint shareholders in a distribution venture called 2 Entertain.
The stores will remain open until after Christmas. However, the company's website has been suspended and is no longer accepting orders.