Smith could be surprised to find himself at the top of this week’s official chart when it is revealed on Friday 2 October.
“I don’t think it’s a number one friendly song if you know what I mean,” Smith told BBC Radio 1’s Nick Grimshaw last week.
“Who knows, but I don’t think it will [get to number one] at all – but I’m not looking for that.”
Other new entries this week include Rudimental and Ed Sheeran’s collaboration Lay It All On Me, currently at number 10, plus Little Mix single Love Me Like You, currently at 14, and Sia’s Alive at 20.
Caracal leads chart
Meanwhile, dance duo Disclosure, who provided production work on Smith’s Bond theme along with songwriter Jimmy Napes, are set to score their second number one album later this week.
Caracal features another collaboration with Smith as well as tracks with The Weeknd, Gregory Porter, Kwabs, Lorde, and Miguel.
Disclosure topped the chart in 2013 with their debut Settle, one of the year’s biggest albums.
Combined sales and streaming figures put it 7,000 copies ahead of nearest rival New Order, who return with their tenth studio album, Music Complete.
Scottish synth-pop group Chvrches are currently at three with their second studio album Every Open Eye.