Danns, 34, has made 21 appearances for the Shakers this season.
Portuguese Correia, 22, has signed at 18-month contract, with a one-year option, having scored 11 goals this season for Northern Premier League North side Radcliffe Borough.
Both players could feature against Colchester on Saturday.
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Blackpool have signed Bury midfielder Neil Danns on loan until the end of the season and Radcliffe Borough striker Raul Correia for an undisclosed fee.