Both these English Premier League clubs have been keen on signing the striker in the summer window just gone, and were also apparently plotting a move for him in January.
The Portugal international is currently on loan at La Liga side Deportivo La Coruna, and this is where his main focus is at the moment.
After that, the 21-year-old is set to do all he can to break his way into the Benfica side, and insists that he is not bothered by the transfer speculation.
Despite not having the best goal-scoring record at the moment, Oliveira is considered as a player with bags of potential that could go on to be one of the world’s leading front-men.
He played a bit part for Portugal in the European Championships, but did not exactly set the tournament alight.
If either one of these English clubs did come in with a substantial offer though, it could be tough for Benfica to turn them down.
We shall see.