"She has written to the board president requesting to play a Twenty20 match for the academy," Indian board secretary Niranjan Shah told Reuters on Tuesday.
"A decision has not been taken yet," he said. "We need to find the time because we've already finalised our schedule."
Woolmer died in Jamaica in March, a day after Pakistan suffered a shock World Cup defeat by debutants Ireland and went out in the first round.
His death was investigated as murder until after the World Cup when Jamaican authorities announced it was due to natural causes.
The former England all-rounder coached South Africa in the 1990s and had settled in the country. Woolmer's family want to bring his academy plans to fruition through a trust fund set up in his memory.