The 25-year-old South American stopper, who hails from Sao Paulo, was believed to be a primary target for the Barclays Premier League outfit during the January transfer window.
Tottenham have also been linked with Blackburn's Christopher Samba, as Redknapp seeks defensive reinforcements to strengthen at the back in a bid to maintain the club's title challenge this year.
However, any hopes the north Londoners may have had of completing a deal for Carvalho now look to have been dashed after Serie A side Genoa confirmed they have beaten off competition for the Figueirense defender.
"Roger Carvalho? He's undergoing medicals, then his signing will be official," confirmed club president Enrico Preziosi to Sky Italia.