It is understood the Blues have lodged an offer to sign 20-year-old Arsenal full-back Traore on loan until the end of the season, while Birmingham are thought to have begun negotiations with Russian side Spartak Moscow over a cut-price deal for versatile defender Jiranek, whose contract expires in December.
Traore, who saw a move to Benfica fall through recently, is Arsene Wenger's third-choice left-back at the Emirates Stadium, behind France international Clichy and highly-rated youngster Kieran Gibbs who made his England debut against Hungary earlier this month.
The Frenchman, who spent last season at Portsmouth, is also believed to be the subject of a bid from Juventus, who are keen to tie up a loan deal with an option to buy at the end of the season.
Towering defender Jiranek, who can play at centre-back or full-back, would add further defensive steel to a Blues squad currently riding high in the Barclays Premier League after an encouraging start.
Ben Foster, Nikola Zigic and Matt Derbyshire have been the most notable arrivals at the club this summer but Blues boss Alex McLeish has been otherwise frustrated in his pursuit of signings to further bolster his squad.
McLeish has seen moves for Moussa Dembele and Charles N'Zogbia fail to materialise, with the former opting to join Fulham and the latter's arrival from Wigan scrapped due to his high wage demands.
The Scot admitted earlier that he is keen on adding fresh faces to his squad before tomorrow's 6pm deadline.
"We are trying our best to bring people in to improve the quality of the squad," McLeish told the club's website.
"The near misses I've had with Dembele, N'Zogbia and others, that's unfortunate when you see how good these players are but there are other ones out there and we'll try and add somebody before six o'clock on Tuesday."
The Birmingham manager also revealed that the knee injury which Sebastian Larsson sustained against Bolton on Sunday is not as bad as first feared.
The former Arsenal man had to be withdrawn deep into the second half after a sturdy challenge involving Bolton captain Kevin Davies, prompting fears that the midfielder could be out for a considerable length of time.
McLeish allayed those concerns this afternoon.
He said: "It's Larsson's knee but we don't think it's as bad as we first thought.
"We thought it may have been a dislocated kneecap, something as severe as that, but it doesn't seem as bad as when he fell on the ground."