The 23-year-old has been linked with a move to England over recent weeks.
Interest has been mooted from Manchester, with Premier League champions City said to be keen on exploring a deal.
Everton, though, has hinted that Old Trafford could be a landing spot for his future.
He believes his game is well suited to life in Europe and has suggested that a switch away from Gremio will soon be made.
Everton told the Daily Mail after finding the target in the colours of his country at the Copa America: “I'm a player that's always trying to get on top [of the opposition].
“Cutting in from the left with dribbles and good finishes.
“Clubs in Europe have this style of play too and maybe I can fit in at Manchester United and others.”
Everton had previously claimed to be “focused only on the national team”.
He was, however, talked into discussing his future.
His comments will have been well received at Old Trafford.
United are in the process of piecing together another summer rebuild, with Ole Gunnar Solskjaer in the market for players of Everton’s promise.
He is likely to face competition, though, if a scramble for the South American’s signature is sparked.
Everton provided another example of what he is capable of when stepping off the bench for Brazil against Bolivia.
He was given just nine minutes in that contest, but was still able to put the seal on a 3-0 win with a spectacular strike .
Gremio are aware of the talent they have on their hands and have made it clear that they will not be forced into a sale.
It may be that they have to drop their demands slightly, but their plan at present is to hold out for an €80 million (£71m/$90m) release clause to be triggered.
They have seen nobody get close to that figure as yet, with club president Romildo Bolzan Junior having said: "At the moment we have no serious and concrete offers for Everton on the table. He is a Gremio heritage, a very important player for us.”