Left winger Jeremy Corbyn is strongly tipped to take over from Ed Miliband, whose inner circle included Mr Khan, MP for Tooting.
Mr Khan, a civil rights lawyer, will hope to replace Boris Johnson at City Hall next May, after overcoming a challenge from former Olympics minister Tessa Jowell in Labour’s mayoral selecttion contest.
Mr Corbyn told Channel 4 News on Wednesday (watch video below) he has already started sounding out fellow MPs over posts in his frontbench team, and has thought about who should become shadow chancellor and shadow foreign secretary.
Asked by Jon Snow if he had names in mind for these key posts, he said: “Of course. There’s lots of things in my head, including that.”
Fellow leadership candidate Liz Kendall, a Blairite, has effectively conceded defeat, ruling out serving in a Corbyn-led shadow cabinet.
But Mr Corbyn said that while many Labour MPs disagreed with him, “they also understand that whoever is elected leader – and we don’t know who it’s going to be – has a mandate that has come from the widest franchise there’s ever been for a Labour party election”.
Under post-Miliband changes to Labour’s leadership election rules, people have been able to become registered supporters of the party for £3 and vote in the contest. It is believed that much of Mr Corbyn’s support has come from these registered supporters.
The same process was used in the mayoral candidate elections, with Mr Khan and Baroness Jowell up against Corbyn supporter Diane Abbott, MP and lawyer David Lammy, former international development minister Gareth Thomas and transport campaigner Christian Wolmar.
Mr Lammy has called for an inquiry into the operation of the contest after claims that as many as one in five potential voters in the capital did not receive their ballot papers by the deadline of noon on Thursday.