The cities are bidding for the Games after Durban was stripped of the event.
Warner says it is more cost effective to use the stadium, which hosted the 2012 Olympics and 2017 World Athletics and Para-athletics Championships.
"The first one to make the call has the knockout bid," he said.
Liverpool's plan will see a temporary athletics track put into Everton's proposed new stadium, while Birmingham is planning on refurbishing Alexander Stadium, the home of the national championships.
"If I was leader of the Liverpool or Birmingham bid I would be ringing [London Mayor] Sadiq Khan and say 'you know what, can we have the athletics in London and we will do everything else?" Warner told BBC Radio 5 live's Sportsweek.
Warner, who is also co-chairman of London 2017, said: "I spoke to a civil servant, who is heavily involved in the Commonwealth Games bid, he said he was going to be 'be rinsing the treasury for half a billion pounds to put on an English Commonwealth Games.'
"My answer is, save a load of money, use this amazing facility, which is the best in the world and make it an English bid."
Liverpool Mayor Joe Anderson told BBC Radio Merseyside: "Liverpool's case is around the fact that - with the athletics village, with the things that we would put in place - there would be a huge legacy, not just economic but for sport, for our children, for the future."
Both cities will be inspected in August, before the final decision in September.
The Department of Culture, Media and Sport will then forward the bid to the Commonwealth Games Federation.
Cities in Canada, Australia and Malaysia are also expected to bid for the Games.
Liverpool and Birmingham should ask to use London Stadium for athletics as part of their 2022 Commonwealth Games bids, says outgoing UK Athletics chief Ed Warner.