The 27-year-old has been put out of the team, following the arrival of Shaun Wright-Phillips at Eastlands.
Elano joined City from Shakhtar Donetsk for £8million last year.
Spurs would face competition from Liverpool, who are also planning to make a move for the Brazilian in January.
Rafael Benitez is ready to offer Yossi Benayoun and Stephen Darby for the Brazilian.
