The newly-issued Polydor track had shifted nearly 97,000 copies up to the end of business on Tuesday, according to the Official Charts Company, more than double that of closest challenger Whistle by Atlantic-signed Flo Rida.
Cole has previously topped the UK singles chart with Fight For This Love in 2009 and Promise This the following year and Call My Name is virtually guaranteed to follow suit.
With sales of the Flo Rida track up 269% on the week, the Decca single Sing by Gary Barlow and the Commonwealth Band is now down to three in the week to date having climbed to number one last Sunday.
Barlow's album of the same name, having secured a second week at the top last weekend, continues to lead the artist albums market this week, but is fewer than 1,000 sales ahead of RCA act Usher's brand new studio set Looking For Myself in second place.
Only a few hundred sales further behind is Life In A Beautiful Light, the third album by Mercury act Amy MacDonald, which is showing up as a new entry at three on artist albums at this stage of the week. Parlophone act Coldplay's Mylo Xyloto climbs 5-4 as Asylum/Atlantic's Ed Sheeran album + drops 2-5 in the week it has been released in North America.
Maximo Park could be heading for their third consecutive Top 10 album but their first on Universal-owned V2 with The National Health currently appearing as a new entry at six, while following a label change themselves from EMI to Domino Hot Chip's newly-released In Our Heads is placed ninth.
The Top 10 sellers at this point of the week are completed by Virgin act Emeli Sande's Our Version Of Events dropping 6-7 and the Reprise/Rhino Bee Gees best of Number Ones falling 4-8, while RCA act Paloma Faith's Fall To Grace slips 3-10.
After being discounted at retail, the four-disc Fleetwood Mac boxed set 25 Years - The Chain, which was first released by Warner Bros in 1992, is new at 12 in the midweeks. Also newly arriving is UK electronic dance music producer and DJ Orlando Higginbottom under the guise of Totally Enormous Extinct Dinosaurs. His Polydor debut Trouble is the 19th top artist seller in the week so far.
Other albums set to debut this Sunday include Bobby Womack's first XL album The Bravest Man In The Universe, Sony best ofs from Johnny Cash and Stone Roses and an album of vintage Neil Young material from Reprise/Warner Bros.
Back on the singles midweeks and a version by Precision Tunes is leading various cash-in covers of Maroon 5's US smash Payphone ahead of its UK release. The PT Records-issued Precision Tunes interpretation has moved 83-14 in the midweeks with around 8,600 sales in the week so far.
Joining Cheryl Cole, Flo Rida and Gary Barlow in the midweek top five is Asylum/Black Butter's former number one Feel The Love by Rudimental featuring John Newman. It holds at four as Parlophone's Coldplay climb 8-5 with Princess Of China featuring Rihanna.
Atlantic/Fueled By Ramen's We Are Young by Fun featuring Janelle Monae drops 3-6 and DJ Fresh featuring Dizzee Rascal's Ministry of Sound-issued The Power slips 6-7. The Top 10 at this stage of the week is completed by three more fallers with RCA act Usher's Scream down 5-8, Interscope/Polydor's Carly Rae Jepsen single Call Me Maybe dropping 7-9 and Rihanna's Def Jam/Mercury cut Where Have You Been slipping 9-10.
A week after The Voice winner Leanne Mitchell's Run To You missed out on a Top 40 place, tracks by other finalists from the BBC One programme are debuting in the midweeks. They are led in 30th place by the Island-issued Steve Winwood cover Higher Love by Tyler James, but also include Max Milner's version of Tom Petty's Free Fallin' and Bo Bruce's reworking of Kate Bush's Running Up That Hill, both on UMTV.
The full midweek singles and albums charts are on musicweek.com.