The Bears are considering how to remember one of their most successful coaches, should plans for a £20m ground redevelopment be approved.
Woolmer, who also coached Pakistan and South Africa, was 58 when he died at the Cricket World Cup in March.
Plans are also being developed to bring the game's biggest stars to Edgbaston for a memorial match on 25 July.
Woolmer, who played Test cricket as a top-order batsman for England, guided Warwickshire to a dream "Treble" in 1994, winning the County Championship, Sunday League and Benson & Hedges Cup.
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Warwickshire ponder Woolmer stand
Warwickshire ponder Woolmer stand
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