Gabigol helped Brazil to win its home Olympics in 2016 and was considered one of the world's hottest young strikers, earning a move to Inter for a reported €25million.
Since then the 21 year-old has flopped in Italy, scoring a single Serie A goal and failing to start any league games, while a loan spell at Benfica has failed to revive Gabigol's career.
Santos president Jose Carlos Peres said talks between the club and Inter over a Brazilian return for Gabigol are now ongoing.
"There's a dialogue under way with Inter," Peres told FPF TV. "We made our offer and now we're waiting for a response. It's all done between ourselves and the player.
"Now it all depends on Inter, who are owned by the Chinese [Suning Group]. We're moving toward an agreement."
Gabigol previously indicated he wanted to stay at Benfica and fight for his place, with the striker still hoping for an unlikely Brazil call-up for the 2018 World Cup.