The 25-year-old Argentinean appears to be heading for the Bernabeu exit with many reports claiming he no longer features in manager Jose Mourinho's plans.
"Gago is a top player and I think he could do well at Inter. It would be like home for him seeing that there are many Argentines there," Simone Picotti, the player's representative is quoted as saying by Tuttomercatoweb.com.
"We have to see what happens with Inter, but we are talking about a club at the top of the list.
"Gago would like to play there."
The Argentina international moved from Boca Juniors to Madrid for €20.4 million, and it had been strongly suggested in the media that he would return to the club on loan.
However, with the transfer window in Argentina coming to a close on Friday, there is little time for all interested parties to come to an agreement.
Gago won two national championships with Boca as a player in 2005 and 2006. He was also part of the Argentina squad which were knocked out of the Copa America 2011 at the quarterfinal stage.