The highly-rated Spanish under-19 international currently plays for Real Madrid's Castilla team in the third division, and was in disputes with 'Los Blancos' over a new contract.
Gomez, 20, saw himself frozen out of the team as a result, but finally renewed the contract in July.
Madrid want to send the forward on loan to gain first-team experience, with Swansea happy to offer that.
The 'Swans' only have one fit striker in their current side - Scottish international Oli McBurnie.