Organisers of Sunday's race are stepping up security to avoid protests after recent disruptions at the Grand National horse race and World Snooker Championship.
A Just Stop Oil protestor halted the World Snooker Championship on Monday after he climbed onto a table and scattered a bag of orange powder paint over the green cloth playing surface.
Saturday's Grand National was delayed by animal rights protesters, with 118 people arrested.
"(Extinction Rebellion) will be uniquely asking all their participants to help guard the London Marathon. To do something that is quite unique in their history – to protect what is one of the crown jewels of British sport," Brasher told British media.
"We run for clean air. That is so important in what we do. The environment is part of our DNA. And Extinction Rebellion has been very, very clear that they are in a new phase of wanting to engage the general public in a different way."
About 750,000 people are expected to attend the race.
Brasher said he was hoping to meet Just Stop Oil representatives in the next 24 hours.
Extinction Rebellion said they had no intention of disrupting the event.
"We acknowledge that the charities and campaigns groups that runners are supporting are unequivocally in favour of acting against climate collapse," the group said in a statement.
"In an emergency, as we are, we must find a way to share the London streets as we all want to support charity, but we also need to hold the government to account."
