The La Liga side are keen to strengthen their defensive ranks for next season and see the Spanish Under-21 player as a good acquisition.
Ibanez is likely to be offered a long-term contract by Inter and the financial terms of their offer may price Atletico out of the running.
One stipulation of any deal is believed to be that the player's agent - Alejandro Camano - retains a 50 percent ownership of Ibanez.
If the Spanish side do miss out on Ibanez it is believed they will then focus their attentions on Colombian stopper Luis Perea.
