"We've got to pick players who are Twenty20 specialists, and Andrew isn't one of those," he told BBC Radio 5 Live.
"All decisions we make about a individual are discussed with that individual and this has been discussed many times throughout the winter, prior to the winter as well, and certainly at a later stage before this announcement so he fully understands where we're coming from."
Strauss decision mutual - England managing director Hugh Morris
Miller said the decision to delay naming a Twenty20 captain had been taken because the selectors felt it was "important to comprehensively review the recent tour of the Caribbean and seek input from all relevant parties including the incoming England team director who is yet to be appointed."
Strauss's predecessor Kevin Pietersen is sure to be one of the names in the frame, although he has already indicated he feels it is too soon for him to take on the job again after quitting as captain in January after a rift with then coach Peter Moores.
Pietersen has, however, accepted the job of skippering Royal Challengers Bangalore in the Indian Premier League, which begins later this month.
"We appreciate it was a difficult time in the winter but as as I'm concerned, the door always remains open. When the director of cricket is appointed, which will be in the next two or three weeks or so, we will sit down and discuss that because the captain is obviously going to be a vital part of that side," Miller said.
He indicated that other possibilities to lead England in the World Twenty20 would be Paul Collingwood and Andrew Flintoff, who have also captained the team in the past, and that Kent skipper Rob Key was also "in the mix".
Key has led Kent to two Twenty20 Cup finals and the 29-year-old admitted he was flattered to be linked with the England job.
"My name has been touted around as captaincy for England for a bit and I never really thought it was going to happen," he told BBC Radio 5 Live.
"But we're in that position again, although I don't know a great deal about what is going on. All I know is I'm in the 30-man squad and we'll see what happens."
Of the new faces in the squad, Denly and Morgan were part of the Kent and Middlesex teams which won the 2007 and 2008 domestic Twenty20 Cup competitions, and Morgan also has international experience with Ireland, while Napier's efforts for Essex have won him an IPL contract with Mumbai Indians.
'Door open' for Pietersen to captain Twenty20 team - Miller
Yorkshire's Rashid was part of England's squad on the tour of the Caribbean, which ended on Friday, without making an appearance, while Woakes, from Warwickshire, is the youngest member of the squad at the age of 20.
The selectors have named three wicketkeepers in the squad with Essex's James Foster, who has not played international cricket for seven years, joining Matt Prior and Steven Davies.
There are also places for 40-year-old Middlesex skipper Shaun Udal and Notts all-rounder Samit Patel, who was recently left out of the squad for the Caribbean after "failing to reach acceptable standards of fitness for international cricket".
Miller said: "We have a wealth of talented players in the 30-man squad who have proved themselves adept at limited overs cricket so there are several options for the selectors to consider before reducing the squad to 15 players at the start of next month.
Woakes played for England in last year's Under-19 World Cup
"We have an encouraging blend of experience and youth in this preliminary squad including a number of uncapped players who will be eager to make their international debut at home during what promises to be an fantastic tournament in June."
England have a poor record in Twenty20 cricket, winning only six of their 15 games so far.
At the inaugural ICC World Twenty20 two years ago, they made it through to the Super Eight stage by virtue of a win over Zimbabwe, but bowed out of the tournament after losing to hosts South Africa, New Zealand and India.
England squad: Kabir Ali (Worcestershire), James Anderson (Lancashire), Gareth Batty (Worcestershire), Ian Bell (Warwickshire), Ravi Bopara (Essex), Tim Bresnan (Yorkshire), Stuart Broad (Nottinghamshire), Paul Collingwood (Durham), Steve Davies (wk, Worcestershire), Joe Denly (Kent), James Foster (wk, Essex), Andrew Flintoff (Lancashire), Steve Harmison (Durham), Rob Key (Kent), Sajid Mahmood (Lancashire), Dimitri Mascarenhas (Hampshire), Eoin Morgan (Middlesex), Graham Napier (Essex), Samit Patel (Nottinghamshire), Kevin Pietersen (Hampshire), Liam Plunkett (Durham), Matt Prior (wk, Sussex), Adil Rashid (Yorkshire), Owais Shah (Middlesex), Ryan Sidebottom (Nottinghamshire), Graeme Swann (Nottinghamshire), Chris Tremlett (Hampshire), Shaun Udal (Middlesex), Chris Woakes (Warwickshire), Luke Wright (Sussex).
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