Flower is presiding over his first selection meeting as official coach
The England selectors have delayed naming the squad for the first Test against West Indies until 29 April.
The squad was due to be announced on Monday, along with an England Lions XI to face the tourists in a four-day match at Derby, starting on 30 April.
But National selector Geoff Miller said: "The selectors have met but have decided we need more time to assess players who are returning after injury.
"It allows us the opportunity to see another round of Championship matches."
The first Test begins at Lord's on 6 May.
The number three batting position remains one of the problem areas for Miller and his selection panel, which also includes new team director Andy Flower, James Whitaker and Ashley Giles.
Former captain Michael Vaughan, who many believe could force his way back into the team for the Ashes, has had only one innings so far this season, when he made 12 for the MCC against reigning county champions Durham at Lord's.
However Ian Bell, who was deposed as number three by Owais Shah during the tour of the West Indies earlier this year, struck 172 against Somerset in his first innings of the new season for Warwickshire.
Meanwhile, Graeme Swann has been carrying an elbow injury in recent weeks and will want to show he is fit to play.
The squad for the ICC World Twenty20 beginning on 1 June will be announced on 1 May, along with the players for the three-match one-day international series against the West Indies, which starts on 21 May.