England lift for Yorkshire pair
Bresnan, who is in Bangladesh for the one-dayers, will replace former Yorkshire left-armer Ryan Sidebottom in the Test squad and Shahzad is hoping for his international one-day debut on Friday for Stuart Broad.
Middlesex seamer Steven Finn, 20, who has been with the Lions in Dubai, has also been drafted in as cover.
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Hide AdSidebottom is to fly home due to a thigh injury while Broad has been ruled out of the final one-day international in Chittagong with a back problem.
Broad sat out today's training session with a back problem he sustained during his second over in Tuesday's series-clinching win but bowled four more before leaving the field for treatment.
Ajmal Shahzad could be drafted in for his ODI debut, although Durham bowler Liam Plunkett is also available.
Finn, 20, will not be involved tomorrow but will link up with the rest of the squad ahead of the first Test on March 12.
The 6ft 7in right-armer has represented England at Under-16, 17, 18 and 19 levels after making his Middlesex debut aged 16 in 2005.