Italian agent believes his Argentine client, who has been linked with a switch to Boca Juniors, could move to the Serie A giants if a return to South America fails
The 25-year-old midfielder is no longer part of coach Jose Mourinho's plans at the Bernabeu and is looking for a way out.
Gago was linked with a move back to Boca Juniors, but the transfer market in Argentina will close on Friday, leaving him with little time to complete a return to South America before the deadline.
But Picotti feels something could still happen in Europe.
"Gago is a top player and I think he could do well at Inter," Picotti is quoted as saying by Tuttomercatoweb.com.
"It would be like home for him seeing that there are many Argentines there.
"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 to the Bernabeu in 2006 for £17.8 million (€20.4m), but despite enjoying a promising start to life at the club, a string of injuries over the past two seasons have restricted him to a peripheral role.