Ramos has caught the eye of several Premier League clubs over the summer with Nottingham Forest and Wolves also circling, but now it appears Newcastle are prepared to put down a proper cash offer.
Portuguese journalist Pedro Sepulveda has reported that Newcastle will make a bid for the 21-year-old in the coming days. Though Benfica expect any club making an approach to hit their valuation, which could be between £25-28million.
However, Benfica might be tempted to increase the price if the young striker continues his superb start to the season.
He scored a hat-trick against Midtjylland in the qualifying stages of the Champions League, grabbed an assist in the other leg of that tie and already has two assists from one match in the Liga Portugal.
Ramos scored eight goals in 46 appearances for Benfica in all competitions last season.
Newcastle having been searching for a new face to support the injury-prone Callum Wilson and Chris Wood, who only has two goals to his name in a black and white shirt.
The Magpies have also been chasing Lyon midfielder Lucas Paqueta and Marseille forward Bamba Dieng in recent days.
Newcastle manager Eddie Howe has always remained guarded about possible targets recently saying: "It's disrespectful to the club that the player represents. We'll do our business in private. There are many teams in Portugal and players we are looking at to find the best ones to make us better."