The 33-year-old Brazilian is third choice at White Hart Lane, behind Hugo Lloris and Brad Friedel, and is keen to play first team football to stake a late claim for a World Cup place.
Gomes has been at Tottenham since 2008, when he signed from PSV Eindhoven for a fee of £7.8million.
He has been out of the first team picture since 2011 when Spurs signed Brad Friedel, and has dropped further down the pecking order since the arrival of Hugo Lloris in the summer of 2012.
He spent last season on loan at Hoffenheim in a bid to add to the 11 caps he already has for his country.
However, despite gaining the captaincy at the Bundesliga outfit, his season was cut short when he broke his hand with a month of the campaign remaining.
Leeds had previously approached Stoke City over the possibility of signing Jack Butland on loan, but manager Brian McDermott has now turned his attentions to Gomes, and hopes to have the deal completed in time for Saturday’s game against Middlesbrough.