Sky sources understand the Magpies are tracking the highly-rated 19-year-old although a deal has yet to be concluded.
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.
The teenager has scored 13 goals in 29 starts for the Sky Bet League Two side, for whom he is due to play in a pre-season friendly at non-league Sileby Rangers on Sunday before the squad travels to a training camp in Brighton.
McClaren arrived at the club three weeks ago and revealed on Friday he had written to the club’s supporters asking for patience as he prepares to reshape his squad.
The former England manager replaced John Carver at the end of last season, after almost two years at Derby, and has promised to keep fans updated on events at St James’ Park throughout the season.
McClaren said: “I know the anticipation is already out there and that you want to see new players coming through the door immediately. That is natural. For me as head coach, however, it is so important that the right players come through the door.
“However long that takes, I want to make sure that we have just the type of people who can come in and force us forward.”