Potential contenders for Liberal Party selection to contest the seat include tech executive and former political adviser Gisele Kapterian and City of Sydney councillor Craig Chung.
“I make this announcement now in fairness to those who may be interested in nominating for party preselection,” Mr Alexander said in an email to supporters and constituents in Bennelong on Friday.
“I care about the future of Bennelong and want the best possible party candidates competing in a fair contest for the honour of potentially representing our community.
“Alongside representing Australia in tennis,serving you and representing our community here in Bennelong has been one of the greatest honours of my life.“
Mr Alexander regained the seat for the Liberals at the 2010 election after Labor swept into power at the 2007 election by toppling former prime minister John Howard,who had held Bennelong since 1974 but lost the seat to Labor candidate and former ABC host Maxine McKew.
“Winning back Bennelong wasn’t easy. But we got there through hard work and perseverance,” Mr Alexander said in his email on Friday.
“Doorknocking over 10,000 homes in the process,I committed to listen,listen and listen again.