Khan said in February he would support the £175m Thames crossing if elected mayor but would closely scrutinise decisions made by his predecessor Boris Johnson in relation to the project.
That process is now underway, a spokesperson for the Mayor of London said.
"The Mayor supports construction of the Garden Bridge but expressed concerns during his election campaign about the way that the procurement process was carried out. He is only in his first days in the role but he is looking in more detail at some of the issues raised about the procurement."
The £175m Thames crossing will also be a public garden, with the landscape designed by Dan Pearson and built by Willerby Landscapes. Construction on the bridge is due to begin in summer.
The bridge has been strongly criticised both for the amount of public funding involved and a bridge design procurement process critics said was neither fair nor transparent.
The Greater London Authority's oversight committee said Johnson had been "less than honest" around his involvement in the procurement process. Both the Garden Bridge Trust and Johnson have strongly denied those accusations.