The Cumbrian-born 35-year-old spent five years at his boyhood club from 2015 to 2019, making just shy of 200 appearances and claiming the captain’s armband for part of his time there.
Previous Blues boss Chris Beech was sacked last night after a 3-0 defeat to Bristol Rovers on Saturday left the Brunton Park side sitting in English League Two’s relegation zone.
BetVictor currently have Grainger placed as favourite for the job at 5/1.
Caretaker boss Gavin Skelton is second in the running at 8/1.
League Two managerial stalwarts Paul Tisdale and John McGreal are both 12/1 with William Hill.
Annan Athletic’s Peter Murphy is another Scottish-based name in the running. Also an ex-Blues defender, he is 12/1 with BetVictor.
Penrith-born Grainger has never hidden his affection for Carlisle or his ambition to manage after a spell in charge of Northern Premier League Division One North West side Workington from 2019 to June this year.
Grainger has played at left-back for Scottish clubs including Heart of Midlothian, Dundee United, Gretna, St Mirren and St Johnstone.
He’s been at the Bairns as head coach Paul Sheerin’s number two for four months.