Murray, who ended a 77-year wait for a British winner of the men's singles title in 2013 before winning again in 2016, retired after the Paris Olympics last year.
Wimbledon hope the statue will be revealed in 2027 during the championship's 150th anniversary.
"We are looking to have a statue of Andy Murray here (Wimbledon) and we're working closely with him and his team," All England Club chair Debbie Jevans told the ainslie + ainslie Performance People podcast.
"The ambition is that we would unveil that at the 150th anniversary of our first Championship, which was 1877.
"He's got to rightly be very involved in that and him and his team will be."
A bronze statue of Fred Perry, the last British men's champion before Murray, was erected at Wimbledon in 1984 to mark the 50th anniversary of his first singles championship.
Tennis greats John McEnroe and Billie Jean King are among those that have previously called for Murray to be honoured in similar fashion at Wimbledon.
