Pool held talks with Davies on Monday and revealed the news in a statement on their official website, www.blackpoolfc.co.uk, amid speculation the 48-year-old Scot could be set to fill the vacancy at his former club Nottingham Forest.
Oyston's statement read: "I would like to place on record that the club met and discussed the manager's position with Billy Davies on Monday evening. Contrary to speculation, I can confirm that the meeting concluded with both parties agreeing to speak again on Tuesday.
"I spoke with Billy on two occasions yesterday and he has decided to follow another opportunity, which is a decision we fully appreciate and understand."
Blackpool are searching for their third manager this season after Ian Holloway's successor Michael Appleton left to take charge of Blackburn last month.
Forest are in a similar position following Alex McLeish's departure, less than six weeks on from replacing sacked ex-Doncaster boss Sean O'Driscoll at the City Ground.
Oyston offered O'Driscoll the chance to become Blackpool manager before he opted to take the reins at Bristol City.
"It has been well documented that we have approached a number of people regarding our managerial vacancy, in order to conduct preliminary discussions and ascertain interest from either party," he added.
"We will continue with this process and we will continue to do so in the correct manner. However, we have only offered the position to one person and, unfortunately, that person decided to accept a position at Bristol City."
Davies managed Forest between January 2009 and June 2011 and twice led them to the Championship play-offs. They lost to Holloway's Blackpool at the semi-final stage on the latter occasion a month before his sacking. The former Dunfermline and Motherwell midfielder, who secured promotion to the top flight for Forest's local rivals Derby in 2007, has been out of work since his Reds dismissal.
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