Real Madrid and Juventus have tentatively opened talks over a loan swap for the January market.
The deal would see both players spend six months at their respective clubs with permanent deals discussed at the end of the season.
Tiago is open to the switch, having also courted interest from Real's Spanish Liga rivals Barcelona this month. However, Saviola will need convincing and has only just rejected a huge offer from Spartak Moscow to move to Russia when the transfer window reopens.
