The right-back, who captains the La Liga side, was believed to be a target for the Premier League new boys ahead of transfer deadline day last Thursday.
In the end, Fulham signed Manchester United full-back Timothy Fosu-Mensah on loan as director of football operations Tony Khan revealed that he "decided to go in a different direction and pursue someone else".
Mallo, who signed a new five-year contract at Celta this week, told Spanish newspaper Marca: "I knew the figures I was going to earn at Fulham, but in life it's not all about money and my aim was to continue at Celta. That's why the deal [to sign a new contract] was so quick and easy."
The Cottagers fell to a 2-0 defeat in their opening game of the Premier League season at home to Crystal Palace.