Sky sources reported at the start of July that Newcastle were tracking the 19-year-old, who came through the youth ranks at Northampton. He will train with the rest of the United squad on Friday and Saturday.
Toney scored 13 goals in 60 games for the League Two club.
Newcastle boss Steve McClaren believes he has a big future and could make him his fourth signing of the summer since he arrived at the club.
Defender Chancel Mbemba, midfielder Georgino Wijnaldum and striker Aleksandar Mitrovic have all joined the club during the current transfer window.
Toney, Northampton’s youngest ever player, was close to joining Wolverhampton Wanderers for a fee in the region of £600,000 in November but the deal fell through due to a failed medical.