Luka Modric won his 163rd cap in Croatia's 1-1 draw with Wales
Play was due to get underway at Old Trafford at 11am local time (1000GMT) but persistent rain led the umpires to take an early lunch at 12:15pm (1115GMT), with no play possible in the morning.
Bangladesh lost all their 10 wickets in a dramatic final session on Saturday as they were bowled out for 216 in reply to England’s 419.
Bangladesh, 203 behind on first innings, were left just four runs of shy of avoiding the follow-on.
Strauss has until 10 minutes before the actual, rather than scheduled, start of play to decide on if he wants to make Bangladesh bat again.
Bangladesh found themselves in trouble despite Tamim Iqbal’s 108 — the left-handed opener’s second century in as many innings after his 103 in England’s eight-wicket first Test win at Lord’s.
Off-spinner Graeme Swann, with five wickets for 76 runs — his first five-wicket Test haul in England — did the bulk of the damage after Bangladesh had been well-placed at 153 for one.
Fast bowler Ajmal Shahzad, on his Test debut, offered good support with three for 45.
England’s total saw Ian Bell make 128. His third hundred in five Tests against Bangladesh took Bell’s average against the Tigers to 158.25.
Bell and Matt Prior (93) shared an England record sixth-wicket stand against Bangladesh of 153.
Luka Modric won his 163rd cap in Croatia's 1-1 draw with Wales
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