NSW are looking for Streak's experience following the announcement by Michael Slater on Wednesday that he would join Steve and Mark Waugh in retirement and the decision of Michael Bevan last week to play for Tasmania.
Those four players combined have scored just under 30,000 first-class runs for their state.
Cricket NSW chief executive David Gilbert on Wednesday said his organisation was "very interested" in securing 30-year-old Streak, who took 202 wickets at 27 in 59 Tests before falling out with the Zimbabwe Cricket Union (ZCU).
Gilbert said NSW had not yet had any discussions with Streak, who is about to start an English County stint with Warwickshire, but was awaiting a response from his agent.
Gilbert said NSW would offer Streak the maximum 90,000 dollars (63,000 USD) state playing contract and felt the new ball bowler and middle order batsman would bring a number of positives to the Blues.
"Streak is certainly somebody we're very interested in from the point of view that our senior player influence has been massively eroded in the last couple of months and more particularly in the last week," Gilbert said.
"We are thin in terms of experience and Streak, who played 59 Tests for his country and has captained his country and virtually been a one-man band for all his Test career, is very appealing."