Team Anna had levelled allegations against Mukherjee, Prime Minister Manmohan Singh and 13 other ministers on May 26 and demanded that a Special Investigation Team should look into these.
Kejriwal said the person who becomes the President should be above board.
Asked whether they consider Ram Jethmalani, who has said that he would like to contest the polls, as a good candidate he said, "I don't want to comment on individuals."
Opposition BJP hit out at Team Anna for seeking an independent probe into allegations made by it against Mukherjee before he contests the poll, saying it should not try to become a "super constitutional authority".
"No one should attempt to become a super constitutional authority by compelling anybody before contesting election to take a no-objection certificate from them. It is unfortunate that such type of sweeping statements are given, which do not bode well for their cause," BJP vice president Mukhtar Abbas Naqvi said.