The Portugal international has endured a tough time at the Nou Camp since arriving in the summer of 2016.
After joining the Catalan giants from Valencia, the 24-year-old failed to live up to his billing.
Game time continues to be hard to come by under new manager Ernesto Valverde.
And Inter are looking to take advantage, according to Spanish outlet Don Balon.
Manchester United, though, have also apparently looked into the possibility of signing Gomes.
Jose Mourinho’s Red Devils were mooted with interest last month.
And Don Balon add United have considered a pursuit.
But Inter are putting a very serious proposal on the table for Gomes to leave Barcelona.
Juventus failed in a bid to land him in the summer, and now their Serie A rivals are ready to swoop.
Inter have jumped to the front of the queue and have money to spend due to their Chinese ownership.
Gomes would also be guaranteed a prominent role in the middle of Inter’s team.
With his options limited at Barcelona, a move could go ahead in January.
It remains to be seen if Manchester United will firm up their interest, with a long-term replacement for veteran Michael Carrick still needed.
