The Conservative politician agreed to stand down earlier this month, after he was found guilty of assaulting a 15-year-old boy in January 2018.
During the trial, jurors heard he forced the teenager to drink gin and tonic before dragging him upstairs and carrying out the attack at a house in Staffordshire.
The Crown Prosecution Service has confirmed the 48-year-old lodged an appeal this week, but he is still due to be sentenced at Southwark Crown Court on May 23.
He became the MP for Wakefield at the 2019 General Election, when he beat Labour former frontbencher Mary Creagh by 3,358 votes.
Labour had held the seat since the 1930s, until Khan’s victory, and they are now determined to win it back after his resignation triggered a by-election.
The party has not selected its candidate yet and no date for election can be set until a written order has been issued by the Government.
Reports had suggested Ms Creagh and former Chancellor Ed Balls were interested in running, but they have both ruled themselves out.
In his resignation letter, Khan said he intended to appeal against the conviction but “legal proceedings could last many more months”.
“I have therefore regrettably come to the conclusion that it is intolerable for constituents to go years without an MP who can amplify their voices in Parliament,” he said.
“Representing them has been the honour of my life, and they deserve better than this. Consequently I am resigning as MP for Wakefield and withdrawing from political life.”
He added: “I am now able to focus entirely on clearing my name.
“As I intend for this to be my only statement, I would like to apologise to my family and community for the humiliation this has caused them.”
His victim reported the attack to Staffordshire Police in 2008, but then decided he did not want to proceed.
However, the Crown Prosecution Service said he decided to press for prosecution after his attacker was elected as an MP in 2019, because “he was concerned that Khan was not fit to be in public office”.