The Brazilian international has lost his first team place at White Hart Lane and is expected to leave in January for regular football.
With Gomes on his way out, Spurs are looking into signing a new shot-stopper and 24-year-old Jimenez seems to fit the bill for Harry Redknapp's side.
The Spanish goalkeeper signed for second division Real Murcia last year after leaving Real Vallodolid for the club.
Should a move materialise, it is expected that the Spaniard will jump at the chance to join Spurs. However, his current club are not keen on losing him mid-sesason.
Brad Friedel currently holds the number one shirt at Spurs.