Arsenal are eager to trim their squad and Jenkinson and Bramall are both free to leave.
And Birmingham boss Harry Redknapp has made his mark by snapping up the pair, report The Mirror.
Jenkinson and Bramall are both heading to the Midlands on season-long loan deals.
Redknapp is eager to bolster his squad ahead of a drive to make the play-offs this term.
Jenkinson has years of Premier League experience following two spells on loan at West Ham.
He's been chased by Crystal Palace but will now drop down to the Championship.
Bramall was signed from non-league Hednesford Town in January but is yet to make his Gunners debut.
Arsenal will hope that 12 months experience in the second tier will get him ready to challenge for a first-team spot at the Emirates.
The Mirror say Birmingham want to finalise the double deal for Jenkinson and Bramall today.
Speaking after Saturday's 1-0 defeat at Stoke, Wenger said he needs to clear the decks before drafting in any new faces.
“I expect to sell players first [before we buy]. We have too many and it is not manageable," he said.
"We have 31, that's too many."
